-
- A few identities
(I)
- by
- Simon Plouffe
- Summer
1993
- All equations are equal to 0 and where found
using pari-Gp with an implementation of the LLL algorithm and
an Interface with MapleV.
-
- Identities : General
case, gamma,
Catalan,
Zeta(3)
and the Polygamma
function
63 Psi(2, 1/3) - 26 Psi(2, 1/4) - 26 Psi(2, 3/4) + 7 Psi(2, 5/6)
_______________________________________________
3 3 1/2 11
56 Pi + 32 Pi 3 + Psi(2, 1/12) - Psi(2, ----)
12
_______________________________________________
3 1/2
- 64 Pi 3 - 9 Psi(2, 1/6) + 63 Psi(2, 2/3)
_______________________________________________
3
- 208 Pi + 16 Psi(2, 1/6) - 13 Psi(2, 1/8) + 16 Psi(2, 5/6) - 13 Psi(2, 5/8)
_______________________________________________
3 3 1/2
16 Pi + 12 Pi 2 + Psi(2, 1/8) - Psi(2, 7/8)
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
3
- 4 Pi - Psi(2, 1/4) + Psi(2, 3/4)
_______________________________________________
- 52 Zeta(3) - 9 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
3 1/2
- 8 Pi 3 - 9 Psi(2, 1/3) + 9 Psi(2, 2/3)
_______________________________________________
3 1/2
8 Pi 3 + 52 Zeta(3) - 54 Psi(2, 1/3) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________
3
- 4 Pi - Psi(2, 1/4) + Psi(2, 3/4)
_______________________________________________
27 Psi(2, 1/4) - 8 Psi(2, 1/6) - Psi(2, 3/4) - Psi(2, 5/12) + Psi(2, 7/12)
_______________________________________________
- 252 Psi(2, 1/3) + 13 Psi(2, 1/8) + 104 Psi(2, 3/4) - 28 Psi(2, 5/6)
+ 13 Psi(2, 5/8)
_______________________________________________
3 3 1/2
- 56 Pi + 32 Pi 3 + Psi(2, 1/6) - 63 Psi(2, 2/3) + Psi(2, 7/12)
11
+ Psi(2, ----)
12
_______________________________________________
3 3 1/2
26 Pi - 8 Pi 3 - 63 Psi(2, 1/3) + 13 Psi(2, 1/4) + 5 Psi(2, 1/6)
_______________________________________________
3
2 Pi + 56 Zeta(3) + Psi(2, 1/4)
_______________________________________________
3 3 1/2
- 26 Pi - 16 Pi 3 - 13 Psi(2, 1/4) + 4 Psi(2, 5/6)
_______________________________________________
- 52 Zeta(3) - 9 Psi(2, 1/3) + Psi(2, 1/6)
_______________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________
- Psi(2, 1/3) + 8 Psi(2, 2/3) - Psi(2, 5/6)
_______________________________________________
3
- 4 Pi - Psi(2, 1/4) + Psi(2, 3/4)
_______________________________________________
- 52 Zeta(3) - 9 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
3 1/2
608 Pi 3 - 3276 Psi(2, 1/4) + 117 Psi(2, 1/12) + 7056 Psi(2, 2/3)
11
- 117 Psi(2, ----)
12
_______________________________________________
3 1/2
8 Pi 3 + Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
3 3 1/2
- 16 Pi + 12 Pi 2 - 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 3/8)
_______________________________________________
- Psi(2, 1/6) + 63 Psi(2, 2/3) - 8 Psi(2, 5/6)
_______________________________________________
3
4 Pi + Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________
3 1/2
- 32 Pi 3 - 364 Psi(2, 1/4) + 13 Psi(2, 1/12) + 14 Psi(2, 5/12)
11
+ Psi(2, ----)
12
_______________________________________________
3 1/2 3 1/2 11
128 Pi 3 - 156 Pi 2 - 4 Psi(2, 5/12) - 4 Psi(2, ----) + 13 Psi(2, 5/8)
12
+ 13 Psi(2, 7/8)
_______________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________
3 1/2 11
- 512 Pi 3 - 504 Psi(2, 1/3) + 9 Psi(2, 5/12) + 9 Psi(2, ----)
12
_______________________________________________
416 Zeta(3) + Psi(2, 1/6) + 9 Psi(2, 2/3)
_______________________________________________
- Psi(2, 1/6) + 63 Psi(2, 2/3) - 8 Psi(2, 5/6)
_______________________________________________
3 3 1/2
16 Pi + 12 Pi 2 + Psi(2, 1/8) - 8 Psi(2, 3/4) + Psi(2, 3/8)
_______________________________________________
3 1/2
- 4 Pi 3 - 234 Zeta(3) - 9 Psi(2, 1/3)
_______________________________________________
3 1/2
- 12 Pi 2 + 448 Zeta(3) + Psi(2, 5/8) + Psi(2, 7/8)
_______________________________________________
3
- 2 Pi - 56 Zeta(3) - Psi(2, 1/4)
_______________________________________________
3
- 14 Pi + 24 Zeta(3) + 9 Psi(2, 1/3) - 7 Psi(2, 1/4) + Psi(2, 5/6)
_______________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
3 1/2
- 8 Pi 3 - 8 Psi(2, 1/3) + Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
- 5824 Psi(2, 1/4) + 215 Psi(2, 1/12) + 504 Psi(2, 2/3) + 208 Psi(2, 5/12)
+ 7 Psi(2, 7/12)
_______________________________________________
3 1/2
- 8 Pi 3 - 63 Psi(2, 2/3) + 9 Psi(2, 5/6)
_______________________________________________
3 1/2
4 Pi 3 + 26 Zeta(3) + 36 Psi(2, 2/3) - 5 Psi(2, 5/6)
_______________________________________________
3 1/2
64 Pi 3 + 63 Psi(2, 1/3) - 9 Psi(2, 5/6)
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
416 Zeta(3) + Psi(2, 1/6) + 9 Psi(2, 2/3)
_______________________________________________
3 1/2
- 28 Pi 3 - 26 Zeta(3) - 4 Psi(2, 1/6) + 27 Psi(2, 2/3)
_______________________________________________
3 1/2 11
- 64 Pi 3 - 8 Psi(2, 1/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
- 52 Zeta(3) - 9 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
52 Zeta(3) + 9 Psi(2, 1/3) - Psi(2, 1/6)
_______________________________________________
3 1/2
8 Pi 3 + Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
32 Zeta(3) - 9 Psi(2, 1/3) + 4 Psi(2, 1/4) + 4 Psi(2, 3/4) - Psi(2, 5/6)
_______________________________________________
3 3 1/2 11
- 52 Pi + 32 Pi 3 + 26 Psi(2, 3/4) - Psi(2, 5/12) - Psi(2, ----)
12
_______________________________________________
- 252 Psi(2, 1/3) + 28 Psi(2, 1/6) + 364 Psi(2, 3/4) - 13 Psi(2, 7/12)
11
- 13 Psi(2, ----)
12
_______________________________________________
3 1/2
4 Pi 3 + 234 Zeta(3) + 9 Psi(2, 1/3)
_______________________________________________
- 8 Psi(2, 1/3) + Psi(2, 1/6) + Psi(2, 2/3)
_______________________________________________
8 Psi(2, 3/4) - Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________
13 Psi(2, 1/4) - 4 Psi(2, 1/6) + 13 Psi(2, 3/4) - 4 Psi(2, 5/6)
_______________________________________________
3
4 Pi + Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________
3
- 2 Pi - 56 Zeta(3) - Psi(2, 1/4)
_______________________________________________
3
- 2 Pi - 56 Zeta(3) - Psi(2, 1/4)
_______________________________________________
3
- 2 Pi + 56 Zeta(3) + Psi(2, 3/4)
_______________________________________________
52 Zeta(3) + 9 Psi(2, 2/3) - Psi(2, 5/6)
_______________________________________________
3 1/2
- 64 Pi 3 - 63 Psi(2, 1/3) + 9 Psi(2, 5/6)
_______________________________________________
3 1/2
12 Pi 2 - 448 Zeta(3) - Psi(2, 5/8) - Psi(2, 7/8)
_______________________________________________
3 1/2
8 Pi 3 + 9 Psi(2, 1/3) - 9 Psi(2, 2/3)
_______________________________________________
- Psi(2, 1/12) + 504 Psi(2, 2/3) - 64 Psi(2, 5/6) - Psi(2, 7/12)
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
3 1/2
- 8 Pi 3 - 8 Psi(2, 1/3) + Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
3 11
- 112 Pi - 63 Psi(2, 1/3) - 7 Psi(2, 5/6) + 2 Psi(2, 7/12) + 2 Psi(2, ----)
12
_______________________________________________
3 1/2
8 Pi 3 + 9 Psi(2, 1/3) - 9 Psi(2, 2/3)
_______________________________________________
3 1/2
32 Pi 3 - 13 Psi(2, 1/4) + Psi(2, 1/12) - 13 Psi(2, 3/4) + Psi(2, 7/12)
_______________________________________________
- 52 Zeta(3) - 9 Psi(2, 1/3) + Psi(2, 1/6)
_______________________________________________
3 1/2
- 864 Pi 3 - 364 Psi(2, 1/4) + 216 Psi(2, 5/6) - 13 Psi(2, 7/12)
11
- 13 Psi(2, ----)
12
_______________________________________________
- Psi(2, 1/12) + 504 Psi(2, 2/3) - 64 Psi(2, 5/6) - Psi(2, 7/12)
_______________________________________________
3 1/2
64 Pi 3 + 63 Psi(2, 1/3) - 9 Psi(2, 5/6)
_______________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________
Psi(2, 1/3) - 8 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
3 1/2
12 Pi 2 + 4 Psi(2, 1/4) + 4 Psi(2, 3/4) - Psi(2, 5/8) - Psi(2, 7/8)
_______________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________
11
- Psi(2, 1/6) + 63 Psi(2, 2/3) - Psi(2, 5/12) - Psi(2, ----)
12
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
3
14 Pi - 28 Zeta(3) + Psi(2, 1/6) - 7 Psi(2, 3/4) + Psi(2, 5/6)
_______________________________________________
- 252 Psi(2, 1/3) + 13 Psi(2, 1/4) + 28 Psi(2, 1/6) + 13 Psi(2, 3/4)
_______________________________________________
- 5824 Psi(2, 1/4) + 215 Psi(2, 1/12) + 504 Psi(2, 2/3) + 208 Psi(2, 5/12)
+ 7 Psi(2, 7/12)
_______________________________________________
- 13608 Psi(2, 1/3) + 728 Psi(2, 1/4) + 189 Psi(2, 1/12) + 215 Psi(2, 7/12)
11
+ 26 Psi(2, ----)
12
_______________________________________________
52 Zeta(3) + 9 Psi(2, 1/3) - Psi(2, 1/6)
_______________________________________________
3 1/2
64 Pi 3 + Psi(2, 1/12) - 8 Psi(2, 5/6) + Psi(2, 7/12)
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
- 13 Psi(2, 1/4) + 252 Psi(2, 2/3) - 13 Psi(2, 3/4) - 28 Psi(2, 5/6)
_______________________________________________
3 1/2
4 Pi 3 + 70 Zeta(3) + 9 Psi(2, 1/6) - Psi(2, 1/12) - 28 Psi(2, 3/4)
11
+ Psi(2, ----)
12
_______________________________________________
3 1/2 11
- 64 Pi 3 - 8 Psi(2, 1/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
Psi(2, 1/6) - 63 Psi(2, 2/3) + 8 Psi(2, 5/6)
_______________________________________________
3
32 Pi + 8 Psi(2, 1/4) - Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________
3 3 1/2
- 56 Pi + 32 Pi 3 - Psi(2, 5/12) + Psi(2, 7/12)
_______________________________________________
- 3024 Zeta(3) - Psi(2, 1/12) - 28 Psi(2, 3/4) - Psi(2, 5/12)
_______________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
- 27 Psi(2, 1/4) + Psi(2, 1/12) + Psi(2, 3/4) + Psi(2, 5/12)
_______________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________
3 1/2
20 Pi 3 + 14 Zeta(3) + 5 Psi(2, 1/6) - Psi(2, 1/8) - 8 Psi(2, 3/4)
- Psi(2, 5/8)
_______________________________________________
- 112 Zeta(3) - Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________
3 11
- 108 Pi - 26 Psi(2, 1/4) + Psi(2, 7/12) + Psi(2, ----)
12
_______________________________________________
3 1/2
- 12 Pi 2 - 448 Zeta(3) - Psi(2, 1/8) - 8 Psi(2, 3/4) + Psi(2, 7/8)
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
3 3 1/2
8 Pi + 4 Pi 3 + 10 Zeta(3) + 9 Psi(2, 1/3) - 4 Psi(2, 3/4)
_______________________________________________
3 1/2 3 1/2
- 128 Pi 3 - 156 Pi 2 - 32 Psi(2, 1/6) + 13 Psi(2, 5/8)
+ 13 Psi(2, 7/8)
_______________________________________________
- 8 Psi(2, 1/3) + Psi(2, 1/6) + Psi(2, 2/3)
_______________________________________________
3
2 Pi + 56 Zeta(3) + Psi(2, 1/4)
_______________________________________________
11
8 Psi(2, 5/6) - Psi(2, 5/12) - Psi(2, ----)
12
_______________________________________________
3
32 Pi + Psi(2, 1/8) - 8 Psi(2, 3/4) + Psi(2, 5/8)
_______________________________________________
3
- 108 Pi - Psi(2, 1/12) + 26 Psi(2, 3/4) - Psi(2, 5/12)
_______________________________________________
- 52 Zeta(3) - 9 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
8 Psi(2, 1/4) - Psi(2, 1/8) - Psi(2, 5/8)
_______________________________________________
3 1/2
- 8 Pi 3 - 9 Psi(2, 1/3) + 9 Psi(2, 2/3)
_______________________________________________
52 Zeta(3) + 9 Psi(2, 2/3) - Psi(2, 5/6)
_______________________________________________
- Psi(2, 1/3) + 8 Psi(2, 2/3) - Psi(2, 5/6)
_______________________________________________
Psi(2, 1/3) - 8 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________
3 1/2
8 Pi 3 + Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
3
2 Pi + 56 Zeta(3) + Psi(2, 1/4)
_______________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________
3 1/2 3 1/2
128 Pi 3 - 156 Pi 2 - 32 Psi(2, 5/6) + 13 Psi(2, 5/8) + 13 Psi(2, 7/8)
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
3 1/2
4 Pi 3 - 26 Zeta(3) + 27 Psi(2, 2/3) - 4 Psi(2, 5/6)
_______________________________________________
416 Zeta(3) + Psi(2, 1/6) + 9 Psi(2, 2/3)
_______________________________________________
8 Psi(2, 3/4) - Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________
3
- 104 Pi - 52 Psi(2, 1/4) + 7 Psi(2, 1/6) + 63 Psi(2, 2/3)
_______________________________________________
52 Zeta(3) + 9 Psi(2, 2/3) - Psi(2, 5/6)
_______________________________________________
- Psi(2, 1/3) + 8 Psi(2, 2/3) - Psi(2, 5/6)
_______________________________________________
Psi(2, 1/3) - 8 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
3 1/2
- 64 Pi 3 - 9 Psi(2, 1/6) + 63 Psi(2, 2/3)
_______________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________
3
4 Pi - 26 Psi(2, 1/4) + Psi(2, 1/12) + Psi(2, 5/12)
_______________________________________________
3
2 Pi + 56 Zeta(3) + Psi(2, 1/4)
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
- 52 Zeta(3) - 9 Psi(2, 1/3) + Psi(2, 1/6)
_______________________________________________
- 416 Zeta(3) - 9 Psi(2, 1/3) - Psi(2, 5/6)
_______________________________________________
3 1/2
- 8 Pi 3 - 9 Psi(2, 1/3) + 9 Psi(2, 2/3)
_______________________________________________
3
2 Pi - 56 Zeta(3) - Psi(2, 3/4)
_______________________________________________
3 1/2
8 Pi 3 + 9 Psi(2, 1/3) - 9 Psi(2, 2/3)
_______________________________________________
3 1/2
- 64 Pi 3 - 9 Psi(2, 1/6) + 63 Psi(2, 2/3)
_______________________________________________
3 1/2
8 Pi 3 + 63 Psi(2, 2/3) - 9 Psi(2, 5/6)
_______________________________________________
3 1/2
64 Pi 3 + 63 Psi(2, 1/3) - 9 Psi(2, 5/6)
_______________________________________________
3 3 1/2 11
504 Pi + 224 Pi 3 + 504 Psi(2, 1/3) - 9 Psi(2, 7/12) - 9 Psi(2, ----)
12
_______________________________________________
3 3 1/2
26 Pi + 16 Pi 3 + 13 Psi(2, 1/4) - 4 Psi(2, 5/6)
_______________________________________________
3
2 Pi - 56 Zeta(3) - Psi(2, 3/4)
_______________________________________________
3
- 32 Pi - 8 Psi(2, 1/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________
3
- 4 Pi - Psi(2, 1/4) + Psi(2, 3/4)
_______________________________________________
- 8 Psi(2, 1/3) + Psi(2, 1/6) + Psi(2, 2/3)
_______________________________________________
3 1/2
8 Pi 3 + Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
3
- 16 Pi - 20 Zeta(3) - 81 Psi(2, 1/3) + 9 Psi(2, 1/6) + Psi(2, 3/8)
+ Psi(2, 7/8)
_______________________________________________
3 1/2
4 Pi 3 - 234 Zeta(3) - 9 Psi(2, 2/3)
_______________________________________________
3 3 1/2
- 234 Pi - 112 Pi 3 - 117 Psi(2, 1/4) + 252 Psi(2, 2/3)
_______________________________________________
3 1/2
- 84 Pi 2 - 126 Psi(2, 1/3) + 8 Psi(2, 1/6) - 7 Psi(2, 1/8)
+ 2 Psi(2, 1/12) - 6 Psi(2, 5/6) + 2 Psi(2, 5/12) + 7 Psi(2, 7/8)
_______________________________________________
52 Zeta(3) + 9 Psi(2, 1/3) - Psi(2, 1/6)
_______________________________________________
3 1/2
8 Pi 3 + Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
Psi(2, 1/3) - 8 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
3 1/2
8 Pi 3 + Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
63 Psi(2, 1/3) - 8 Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
3 11
- 56 Pi + 1872 Zeta(3) + 72 Psi(2, 1/3) - Psi(2, 1/12) + Psi(2, ----)
12
_______________________________________________
3
14 Pi + 24 Zeta(3) + 9 Psi(2, 1/3) - 7 Psi(2, 3/4) + Psi(2, 5/6)
_______________________________________________
- 728 Psi(2, 1/4) + 189 Psi(2, 1/6) + 1701 Psi(2, 2/3) - 26 Psi(2, 7/12)
11
- 26 Psi(2, ----)
12
_______________________________________________
3 1/2
- 8 Pi 3 - Psi(2, 1/6) + Psi(2, 5/6)
_______________________________________________
3 1/2
8 Pi 3 + Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
3
4 Pi + Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________
3
2 Pi - 56 Zeta(3) - Psi(2, 3/4)
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
3
26 Pi - 14 Psi(2, 1/3) + 13 Psi(2, 1/4) - 14 Psi(2, 2/3)
_______________________________________________
3 1/2
28 Pi 3 + 26 Zeta(3) + 4 Psi(2, 1/6) - 27 Psi(2, 2/3)
_______________________________________________
3 1/2
- 4 Pi 3 - 234 Zeta(3) - 9 Psi(2, 1/3)
_______________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
3 1/2
32 Pi 3 + 13 Psi(2, 1/4) + 13 Psi(2, 3/4) - 8 Psi(2, 5/6)
_______________________________________________
28 Psi(2, 1/3) - 13 Psi(2, 1/4) + 28 Psi(2, 2/3) - 13 Psi(2, 3/4)
_______________________________________________
- 13 Psi(2, 1/4) + 252 Psi(2, 2/3) - 13 Psi(2, 3/4) - 28 Psi(2, 5/6)
_______________________________________________
52 Zeta(3) + Psi(2, 1/3) + Psi(2, 2/3)
_______________________________________________
3 3 1/2
6 Pi - 4 Pi 3 + 14 Zeta(3) - 3 Psi(2, 3/4) + Psi(2, 5/6)
_______________________________________________
8 Psi(2, 3/4) - Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________
Psi(2, 1/3) - 8 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
- 528 Zeta(3) - 28 Psi(2, 1/4) + 432 Psi(2, 2/3) - 6 Psi(2, 5/12)
11
- Psi(2, 7/12) - 7 Psi(2, ----)
12
_______________________________________________
3 1/2
224 Pi 3 + 117 Psi(2, 1/4) - 504 Psi(2, 2/3) + 117 Psi(2, 3/4)
_______________________________________________
- 364 Zeta(3) - Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
3
2 Pi - 56 Zeta(3) - Psi(2, 3/4)
_______________________________________________
3 1/2 11
512 Pi 3 + 504 Psi(2, 1/3) - 9 Psi(2, 5/12) - 9 Psi(2, ----)
12
_______________________________________________
- 8 Psi(2, 1/3) + Psi(2, 1/6) + Psi(2, 2/3)
_______________________________________________
3 1/2
- 4 Pi 3 + 182 Zeta(3) + Psi(2, 5/6)
_______________________________________________
3 1/2
4 Pi 3 - 234 Zeta(3) - 9 Psi(2, 2/3)
_______________________________________________
896 Zeta(3) + 8 Psi(2, 1/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________
3 3 1/2 11
56 Pi + 32 Pi 3 + Psi(2, 1/12) - Psi(2, ----)
12
_______________________________________________
11
8 Psi(2, 5/6) - Psi(2, 5/12) - Psi(2, ----)
12
_______________________________________________
63 Psi(2, 1/3) - Psi(2, 1/12) - Psi(2, 5/6) - Psi(2, 7/12)
_______________________________________________
3 1/2
- 8 Pi 3 - Psi(2, 1/6) + Psi(2, 5/6)
_______________________________________________
3 1/2 11
- 512 Pi 3 - 504 Psi(2, 1/3) + 9 Psi(2, 5/12) + 9 Psi(2, ----)
12
_______________________________________________
3
16 Pi - 448 Zeta(3) - Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
11
- Psi(2, 1/4) + 27 Psi(2, 3/4) - Psi(2, 7/12) - Psi(2, ----)
12
_______________________________________________
8 Zeta(3) - 2 Psi(2, 1/3) + Psi(2, 1/4) - 2 Psi(2, 2/3) + Psi(2, 3/4)
_______________________________________________
3 1/2
- 4 Pi 3 - 10 Zeta(3) - 9 Psi(2, 1/3) + 2 Psi(2, 1/4) + 2 Psi(2, 3/4)
_______________________________________________
3 3 1/2
- 56 Pi + 32 Pi 3 - Psi(2, 5/12) + Psi(2, 7/12)
_______________________________________________
3 1/2
8 Pi 3 + 9 Psi(2, 1/3) - 9 Psi(2, 2/3)
_______________________________________________
3
4 Pi + Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________
8 Psi(2, 3/4) - Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________
64 Psi(2, 1/3) - Psi(2, 1/12) - 8 Psi(2, 2/3) - Psi(2, 7/12)
_______________________________________________
3 1/2
- 4 Pi 3 + 234 Zeta(3) + 9 Psi(2, 2/3)
_______________________________________________
- 3024 Zeta(3) - Psi(2, 1/12) - 28 Psi(2, 3/4) - Psi(2, 5/12)
_______________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________
3 1/2
- 28 Pi 3 + 26 Zeta(3) - 27 Psi(2, 1/3) + 4 Psi(2, 5/6)
_______________________________________________
11
Psi(2, 1/4) - 27 Psi(2, 3/4) + Psi(2, 7/12) + Psi(2, ----)
12
_______________________________________________
8 Psi(2, 3/4) - Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________
3 1/2
64 Pi 3 + 63 Psi(2, 1/3) - 9 Psi(2, 5/6)
_______________________________________________
3 3 1/2
- 16 Pi + 12 Pi 2 + Psi(2, 3/8) - Psi(2, 5/8)
_______________________________________________
63 Psi(2, 1/3) - Psi(2, 1/12) - Psi(2, 5/6) - Psi(2, 7/12)
_______________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________
8 Psi(2, 1/4) - Psi(2, 1/8) - Psi(2, 5/8)
_______________________________________________
3 1/2
- 864 Pi 3 + 364 Psi(2, 1/4) - 112 Psi(2, 1/6) - 13 Psi(2, 1/12)
11
+ 13 Psi(2, ----)
12
_______________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
3
2 Pi - 56 Zeta(3) - Psi(2, 3/4)
_______________________________________________
3 3 1/2
234 Pi - 112 Pi 3 - 252 Psi(2, 1/3) + 117 Psi(2, 1/4)
_______________________________________________
- Psi(2, 1/3) + 8 Psi(2, 2/3) - Psi(2, 5/6)
_______________________________________________
3
- 4 Pi - Psi(2, 1/4) + Psi(2, 3/4)
_______________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
3 1/2 3 1/2
128 Pi 3 + 156 Pi 2 + 13 Psi(2, 1/8) - 32 Psi(2, 5/6) + 13 Psi(2, 3/8)
_______________________________________________
- 64 Psi(2, 1/3) + Psi(2, 1/12) + 8 Psi(2, 2/3) + Psi(2, 7/12)
_______________________________________________
- 52 Zeta(3) - 9 Psi(2, 1/3) + Psi(2, 1/6)
_______________________________________________
3 1/2
- 8 Pi 3 - 63 Psi(2, 2/3) + 9 Psi(2, 5/6)
_______________________________________________
- 52 Zeta(3) - Psi(2, 1/3) - Psi(2, 2/3)
_______________________________________________
3
- 104 Pi - 7 Psi(2, 1/6) - 63 Psi(2, 2/3) + 52 Psi(2, 3/4)
_______________________________________________
3 1/2
8 Pi 3 - 52 Zeta(3) + Psi(2, 1/6) - 9 Psi(2, 2/3)
_______________________________________________
3 1/2
- 8 Pi 3 - 9 Psi(2, 1/3) + 9 Psi(2, 2/3)
_______________________________________________
3 1/2
- 1792 Pi 3 - 117 Psi(2, 1/8) + 4032 Psi(2, 2/3) - 936 Psi(2, 3/4)
- 117 Psi(2, 5/8)
_______________________________________________
3 3 1/2
- 26 Pi + 16 Pi 3 - 13 Psi(2, 1/4) + 4 Psi(2, 1/6)
_______________________________________________
3 1/2
12 Pi 2 - 448 Zeta(3) - Psi(2, 5/8) - Psi(2, 7/8)
_______________________________________________
80 Zeta(3) - 29 Psi(2, 1/4) + Psi(2, 1/12) + 72 Psi(2, 2/3) - 29 Psi(2, 3/4)
+ Psi(2, 7/12)
_______________________________________________
3 1/2
8 Pi 3 + Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
3 1/2
324 Pi 2 - 104 Psi(2, 1/4) + 27 Psi(2, 1/8) + 4 Psi(2, 7/12)
11
+ 4 Psi(2, ----) - 27 Psi(2, 7/8)
12
_______________________________________________
11
- 3328 Zeta(3) - 72 Psi(2, 1/3) - Psi(2, 5/12) - Psi(2, ----)
12
_______________________________________________
3 1/2 3 1/2
896 Pi 3 - 1404 Pi 2 + 2016 Psi(2, 1/3) - 117 Psi(2, 1/8)
- 117 Psi(2, 3/8)
_______________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________
- 216 Psi(2, 1/6) + 91 Psi(2, 1/8) - 216 Psi(2, 5/6) + 26 Psi(2, 7/12)
11
+ 26 Psi(2, ----) + 91 Psi(2, 5/8)
12
_______________________________________________
- 64 Psi(2, 1/3) + Psi(2, 1/12) + 8 Psi(2, 2/3) + Psi(2, 7/12)
_______________________________________________
3 3 1/2 11
56 Pi + 32 Pi 3 + Psi(2, 1/12) - Psi(2, ----)
12
_______________________________________________
3 1/2
8 Pi 3 + Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
- 364 Zeta(3) - Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
3 1/2
4 Pi 3 + 26 Zeta(3) - 27 Psi(2, 1/3) + 4 Psi(2, 1/6)
_______________________________________________
- 504 Psi(2, 1/3) + 215 Psi(2, 1/4) + 19 Psi(2, 3/4) - 7 Psi(2, 5/12)
+ 7 Psi(2, 7/12)
_______________________________________________
3 11
104 Pi + 8 Psi(2, 1/6) - 52 Psi(2, 3/4) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
- Psi(2, 1/12) + 504 Psi(2, 2/3) - 64 Psi(2, 5/6) - Psi(2, 7/12)
_______________________________________________
Psi(2, 1/6) - 63 Psi(2, 2/3) + 8 Psi(2, 5/6)
_______________________________________________
11
8 Psi(2, 5/6) - Psi(2, 5/12) - Psi(2, ----)
12
_______________________________________________
13 Psi(2, 1/4) - 4 Psi(2, 1/6) + 13 Psi(2, 3/4) - 4 Psi(2, 5/6)
_______________________________________________
3
- 2 Pi - 56 Zeta(3) - Psi(2, 1/4)
_______________________________________________
3 1/2
24 Pi 2 - 8 Psi(2, 1/4) + 2 Psi(2, 1/8) + Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________
3 1/2
- 28 Pi 3 + 26 Zeta(3) - 27 Psi(2, 1/3) + 4 Psi(2, 5/6)
_______________________________________________
3
112 Pi + Psi(2, 1/12) - 8 Psi(2, 5/6) + 2 Psi(2, 5/12) - Psi(2, 7/12)
_______________________________________________
3
- 26 Pi - 14 Psi(2, 1/3) - 14 Psi(2, 2/3) + 13 Psi(2, 3/4)
_______________________________________________
11
3328 Zeta(3) + 72 Psi(2, 1/3) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
- 504 Psi(2, 2/3) + 728 Psi(2, 3/4) + 7 Psi(2, 5/12) - 26 Psi(2, 7/12)
11
- 19 Psi(2, ----)
12
_______________________________________________
- 8 Psi(2, 1/3) + Psi(2, 1/6) + Psi(2, 2/3)
_______________________________________________
3 1/2
- 8 Pi 3 - 8 Psi(2, 1/3) + Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
3 1/2
- 4 Pi 3 - 182 Zeta(3) - Psi(2, 1/6)
_______________________________________________
3 1/2
- 64 Pi 3 - 9 Psi(2, 1/6) + 63 Psi(2, 2/3)
_______________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
- Psi(2, 1/6) + 63 Psi(2, 2/3) - 8 Psi(2, 5/6)
_______________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
4 Psi(2, 1/6) - 364 Psi(2, 3/4) + 4 Psi(2, 5/6) + 13 Psi(2, 7/12)
11
+ 13 Psi(2, ----)
12
_______________________________________________
3
2 Pi - 56 Zeta(3) - Psi(2, 3/4)
_______________________________________________
3 1/2 3 1/2
896 Pi 3 + 1404 Pi 2 + 117 Psi(2, 1/8) - 2016 Psi(2, 2/3)
+ 117 Psi(2, 3/8)
_______________________________________________
Psi(2, 1/3) - 8 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
- 13 Psi(2, 1/4) + 252 Psi(2, 2/3) - 13 Psi(2, 3/4) - 28 Psi(2, 5/6)
_______________________________________________
3 1/2
36 Pi 3 - 26 Zeta(3) + 5 Psi(2, 1/6) - 36 Psi(2, 2/3)
_______________________________________________
3328 Zeta(3) + Psi(2, 1/12) + 72 Psi(2, 2/3) + Psi(2, 7/12)
_______________________________________________
8 Psi(2, 3/4) - Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________
- 504 Psi(2, 1/3) + 215 Psi(2, 1/4) + 19 Psi(2, 3/4) - 7 Psi(2, 5/12)
+ 7 Psi(2, 7/12)
_______________________________________________
63 Psi(2, 1/3) - 26 Psi(2, 1/4) - 26 Psi(2, 3/4) + 7 Psi(2, 5/6)
_______________________________________________
3 11
- 104 Pi + 112 Zeta(3) - 3 Psi(2, 1/8) + Psi(2, 7/12) + Psi(2, ----)
12
- 3 Psi(2, 5/8)
_______________________________________________
- 52 Zeta(3) - 9 Psi(2, 1/3) + Psi(2, 1/6)
_______________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________
3
4 Pi + Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________
- 8 Psi(2, 1/3) + Psi(2, 1/6) + Psi(2, 2/3)
_______________________________________________
3 1/2
64 Pi 3 - 504 Psi(2, 1/3) + 9 Psi(2, 1/12) + 9 Psi(2, 7/12)
_______________________________________________
3 1/2
- 4 Pi 3 + 234 Zeta(3) + 9 Psi(2, 2/3)
_______________________________________________
Psi(2, 1/3) - 8 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
- 8 Psi(2, 1/3) + Psi(2, 1/6) + Psi(2, 2/3)
_______________________________________________
Psi(2, 1/3) - 8 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
- Psi(2, 1/6) + 63 Psi(2, 2/3) - 8 Psi(2, 5/6)
_______________________________________________
3 1/2
- 4 Pi 3 + 182 Zeta(3) + Psi(2, 5/6)
______________________________
3 1/2
- 4 Pi 3 + 26 Zeta(3) - 27 Psi(2, 2/3) + 4 Psi(2, 5/6)
_______________________________________________
17
- 27 Psi(2, 1/8) + Psi(2, 3/8) + Psi(2, 1/24) + Psi(2, ----)
24
_______________________________________________
3
4 Pi + Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________
19
- 8 Psi(2, 7/12) + Psi(2, ----) + Psi(2, 7/24)
24
_______________________________________________
3 3 1/2
234 Pi - 112 Pi 3 - 252 Psi(2, 1/3) + 117 Psi(2, 1/4)
_______________________________________________
19 11
- Psi(2, 1/8) + 27 Psi(2, 3/8) - Psi(2, ----) - Psi(2, ----)
24 24
_______________________________________________
- 52 Zeta(3) - 9 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
3 3 1/2
26 Pi - 16 Pi 3 + 13 Psi(2, 1/4) - 4 Psi(2, 1/6)
_______________________________________________
- 8 Psi(2, 1/3) + Psi(2, 1/6) + Psi(2, 2/3)
_______________________________________________
3 1/2
- 4 Pi 3 - 234 Zeta(3) - 9 Psi(2, 1/3)
_______________________________________________
- 7 Psi(2, 1/3) + Psi(2, 1/6) - 7 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
3 1/2
- 1792 Pi 3 - 117 Psi(2, 1/8) + 4032 Psi(2, 2/3) - 936 Psi(2, 3/4)
- 117 Psi(2, 5/8)
_______________________________________________
3 1/2
8 Pi 3 - 63 Psi(2, 1/3) + 9 Psi(2, 1/6)
_______________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________
3 1/2
- 8 Pi 3 - 9 Psi(2, 1/3) + 9 Psi(2, 2/3)
_______________________________________________
23
- Psi(2, 5/8) + 27 Psi(2, 7/8) - Psi(2, ----) - Psi(2, 7/24)
24
_______________________________________________
- 63 Psi(2, 1/3) + 8 Psi(2, 1/6) + Psi(2, 5/6)
_______________________________________________
Psi(2, 1/12) - 728 Psi(2, 3/4) + 216 Psi(2, 5/6) - 26 Psi(2, 5/12)
+ 27 Psi(2, 7/12)
_______________________________________________
- 63 Psi(2, 1/3) + 26 Psi(2, 1/4) + 26 Psi(2, 3/4) - 7 Psi(2, 5/6)
_______________________________________________
- 52 Zeta(3) - 9 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
- 8 Psi(2, 1/3) + Psi(2, 1/6) + Psi(2, 2/3)
_______________________________________________
- Psi(2, 1/3) + 8 Psi(2, 2/3) - Psi(2, 5/6)
_______________________________________________
3 1/2
- 4 Pi 3 + 234 Zeta(3) + 9 Psi(2, 2/3)
_______________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________
3 1/2
64 Pi 3 + 9 Psi(2, 1/6) - 63 Psi(2, 2/3)
_______________________________________________
11 17
23296 Zeta(3) + 64 Psi(2, 1/6) + 8 Psi(2, ----) + Psi(2, 5/24) + Psi(2, ----)
12 24
_______________________________________________
3 11
4 Pi + 26 Psi(2, 3/4) - Psi(2, 7/12) - Psi(2, ----)
12
_______________________________________________
3 1/2
- 28 Pi 3 + 26 Zeta(3) - 27 Psi(2, 1/3) + 4 Psi(2, 5/6)
_______________________________________________
Psi(2, 1/6) - 63 Psi(2, 2/3) + 8 Psi(2, 5/6)
_______________________________________________
3 11
56 Pi - 1872 Zeta(3) - 72 Psi(2, 1/3) + Psi(2, 1/12) - Psi(2, ----)
12
_______________________________________________
3 1/2
8 Pi 3 + 9 Psi(2, 1/3) - 9 Psi(2, 2/3)
_______________________________________________
11
8 Psi(2, 5/6) - Psi(2, 5/12) - Psi(2, ----)
12
_______________________________________________
3 3 1/2
- 1872 Pi + 896 Pi 3 - 2016 Psi(2, 2/3) + 117 Psi(2, 3/8)
+ 117 Psi(2, 7/8)
_______________________________________________
52 Zeta(3) + 9 Psi(2, 2/3) - Psi(2, 5/6)
_______________________________________________
- 63 Psi(2, 1/3) + 8 Psi(2, 1/6) + Psi(2, 5/6)
_______________________________________________
3 1/2
4 Pi 3 + 26 Zeta(3) - 27 Psi(2, 1/3) + 4 Psi(2, 1/6)
_______________________________________________
19
8 Psi(2, 7/12) - Psi(2, ----) - Psi(2, 7/24)
24
_______________________________________________
- 112 Zeta(3) - Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________
3
104 Pi + 63 Psi(2, 1/3) - 52 Psi(2, 3/4) + 7 Psi(2, 5/6)
_______________________________________________
3 1/2
8 Pi 3 + 9 Psi(2, 1/3) - 9 Psi(2, 2/3)
_______________________________________________
- 52 Zeta(3) - Psi(2, 1/3) - Psi(2, 2/3)
_______________________________________________
13 Psi(2, 1/4) - 252 Psi(2, 2/3) + 13 Psi(2, 3/4) + 28 Psi(2, 5/6)
_______________________________________________
52 Zeta(3) + 9 Psi(2, 1/3) - Psi(2, 1/6)
_______________________________________________
3 3 1/2
26 Pi - 16 Pi 3 + 13 Psi(2, 1/4) - 4 Psi(2, 1/6)
_______________________________________________
17
- 8 Psi(2, 5/12) + Psi(2, 5/24) + Psi(2, ----)
24
_______________________________________________
52 Zeta(3) + 9 Psi(2, 1/3) - Psi(2, 1/6)
_______________________________________________
- Psi(2, 1/6) + 63 Psi(2, 2/3) - 8 Psi(2, 5/6)
_______________________________________________
3 1/2
- 4 Pi 3 + 234 Zeta(3) + 9 Psi(2, 2/3)
_______________________________________________
112 Zeta(3) + Psi(2, 1/4) + Psi(2, 3/4)
bytes used=1000340, alloc=262096, time=1.28
_______________________________________________
- 224 Psi(2, 1/3) + 104 Psi(2, 1/4) - 224 Psi(2, 2/3) + 13 Psi(2, 3/8)
+ 13 Psi(2, 7/8)
_______________________________________________
364 Zeta(3) + Psi(2, 1/6) + Psi(2, 5/6)
_______________________________________________
63 Psi(2, 1/3) - 8 Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
3 1/2
- 8 Pi 3 - 63 Psi(2, 2/3) + 9 Psi(2, 5/6)
_______________________________________________
3
- 4 Pi - Psi(2, 1/4) + Psi(2, 3/4)
_______________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________
13
- 8 Psi(2, 1/12) + Psi(2, 1/24) + Psi(2, ----)
24
_______________________________________________
3
4 Pi - 26 Psi(2, 1/4) + Psi(2, 1/12) + Psi(2, 5/12)
_______________________________________________
19
- 8 Psi(2, 7/12) + Psi(2, ----) + Psi(2, 7/24)
24
_______________________________________________
19
8 Psi(2, 7/12) - Psi(2, ----) - Psi(2, 7/24)
24
_______________________________________________
- Psi(2, 1/3) + 8 Psi(2, 2/3) - Psi(2, 5/6)
_______________________________________________
Psi(2, 1/3) - 8 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________
19 11
Psi(2, 1/8) - 27 Psi(2, 3/8) + Psi(2, ----) + Psi(2, ----)
24 24
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
13
- 8 Psi(2, 1/12) + Psi(2, 1/24) + Psi(2, ----)
24
_______________________________________________
3 3 1/2 11
56 Pi + 32 Pi 3 + 8 Psi(2, 1/6) - Psi(2, 7/12) - Psi(2, ----)
12
_______________________________________________
3 3 1/2
- 26 Pi - 16 Pi 3 - 4 Psi(2, 1/6) + 13 Psi(2, 3/4)
_______________________________________________
Psi(2, 1/6) - 63 Psi(2, 2/3) + 8 Psi(2, 5/6)
_______________________________________________
3 1/2
64 Pi 3 + 63 Psi(2, 1/3) - 9 Psi(2, 5/6)
_______________________________________________
19
24192 Zeta(3) + 28 Psi(2, 1/8) + 27 Psi(2, 5/8) + 27 Psi(2, 7/8) + Psi(2, ----)
24
11
+ Psi(2, ----)
24
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________
3
4 Pi + Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________
3
108 Pi + Psi(2, 1/12) - 26 Psi(2, 3/4) + Psi(2, 5/12)
_______________________________________________
15 Psi(1, 2/3) - Psi(1, 1/6) - 4 Psi(1, 5/6)
________________________________________________
2 1/2
- 2 Pi 2 + Psi(1, 1/8) - Psi(1, 3/8) - 32 Catalan
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
- 4 Psi(1, 3/4) + Psi(1, 3/8) + Psi(1, 7/8)
________________________________________________
2 1/2
- 4 Pi 3 + 15 Psi(1, 1/3) - 7 Psi(1, 1/6) + 5 Psi(1, 1/8) + 5 Psi(1, 5/8)
- Psi(1, 1/12) - 3 Psi(1, 5/12)
________________________________________________
2 1/2
- 10 Psi(1, 1/4) + 5 Psi(1, 1/5) + 5 Psi(1, 4/5) + 80 Catalan - 2 Pi 5
________________________________________________
2 1/2
2 Pi 3 + 30 Psi(1, 2/3) - 8 Psi(1, 5/6) - Psi(1, 1/12) + 40 Catalan
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
- 15 Psi(1, 1/3) + 16 Psi(1, 3/4) - 3 Psi(1, 5/6) + 128 Catalan
________________________________________________
2 1/2
2 Pi 2 + 15 Psi(1, 2/3) - 3 Psi(1, 5/6) - Psi(1, 1/8) - Psi(1, 7/8)
________________________________________________
15 Psi(1, 2/3) - Psi(1, 1/6) - 4 Psi(1, 5/6)
________________________________________________
- Psi(1, 1/4) + Psi(1, 3/4) + 16 Catalan
________________________________________________
15 Psi(1, 1/3) - 2 Psi(1, 1/4) - 2 Psi(1, 3/4) - 3 Psi(1, 1/6)
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
2 1/2
- 8 Pi 3 - 47 Psi(1, 1/3) - 7 Psi(1, 2/3) + 20 Psi(1, 3/4)
+ 4 Psi(1, 1/12)
________________________________________________
15 Psi(1, 1/3) - 4 Psi(1, 1/6) - Psi(1, 5/6)
________________________________________________
2 1/2
- 2 Pi 3 + 30 Psi(1, 2/3) - 16 Psi(1, 3/4) - 2 Psi(1, 5/12) + Psi(1, 7/12)
- 8 Catalan
________________________________________________
11
- 4 Psi(1, 5/6) + Psi(1, 5/12) + Psi(1, ----)
12
________________________________________________
2
- 4 Pi + 3 Psi(1, 1/3) + 3 Psi(1, 2/3)
________________________________________________
40 Psi(1, 1/5) + 40 Psi(1, 4/5) - 20 Psi(1, 5/6) - 5 Psi(1, 1/12)
2 1/2
- 5 Psi(1, 7/12) - 16 Pi 5
________________________________________________
2
- Pi + Psi(1, 3/4) + 8 Catalan
________________________________________________
2 1/2
- 2 Pi 2 + 4 Psi(1, 1/4) - Psi(1, 3/8) - Psi(1, 5/8) - 32 Catalan
________________________________________________
15 Psi(1, 2/3) - Psi(1, 1/6) - 4 Psi(1, 5/6)
________________________________________________
- 15 Psi(1, 2/3) - 3 Psi(1, 1/6) + 4 Psi(1, 1/8) + 4 Psi(1, 5/8) - 128 Catalan
________________________________________________
2 1/2
4 Pi 3 - 15 Psi(1, 1/3) + Psi(1, 5/6) + 2 Psi(1, 7/12) + 80 Catalan
________________________________________________
2
- 16 Pi + 4 Psi(1, 5/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
Psi(1, 1/4) - Psi(1, 3/4) - 16 Catalan
________________________________________________
11
- 4 Psi(1, 5/6) + Psi(1, 5/12) + Psi(1, ----)
12
________________________________________________
2 1/2 2
- 2 Pi 3 - 4 Pi - 2 Psi(1, 1/6) + Psi(1, 3/8) + Psi(1, 7/8)
+ Psi(1, 1/12) - 8 Catalan
________________________________________________
3 Psi(1, 1/3) + 3 Psi(1, 2/3) - 4 Psi(1, 3/4) - 32 Catalan
________________________________________________
2 1/2 11
4 Pi 3 - 30 Psi(1, 2/3) + 10 Psi(1, 5/6) + Psi(1, 7/12) - Psi(1, ----)
12
________________________________________________
Psi(1, 1/3) - 4 Psi(1, 2/3) + Psi(1, 5/6)
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
2 1/2
2 Pi 2 + 15 Psi(1, 1/3) - 3 Psi(1, 1/6) - Psi(1, 1/8) - Psi(1, 7/8)
________________________________________________
Psi(1, 1/4) - Psi(1, 3/4) - 16 Catalan
________________________________________________
2
- 2 Pi + Psi(1, 1/4) + Psi(1, 3/4)
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
2 1/2
- 2 Pi 3 + 5 Psi(1, 1/3) - 5 Psi(1, 2/3) + 4 Psi(1, 3/4) - Psi(1, 7/12)
- 8 Catalan
________________________________________________
- 4 Psi(1, 5/6) + 2 Psi(1, 1/8) + 2 Psi(1, 5/8) + Psi(1, 5/12) - Psi(1, 7/12)
- 144 Catalan
________________________________________________
2 1/2 2
2 Pi 3 - 5 Pi + 5 Psi(1, 1/4) - 2 Psi(1, 1/6) + Psi(1, 7/12)
________________________________________________
- 15 Psi(1, 1/3) + 3 Psi(1, 1/6) + Psi(1, 3/8) + Psi(1, 7/8) + 32 Catalan
________________________________________________
2
- 4 Pi + Psi(1, 1/6) + Psi(1, 5/6)
________________________________________________
2 1/2
6 Pi 3 - 30 Psi(1, 1/3) + 8 Psi(1, 3/4) + 3 Psi(1, 7/12) + 184 Catalan
________________________________________________
- Psi(1, 1/4) + Psi(1, 3/4) + 16 Catalan
________________________________________________
2 11
18 Pi - 10 Psi(1, 1/4) - Psi(1, 7/12) - Psi(1, ----)
12
________________________________________________
2 1/2 11
4 Pi 3 - 10 Psi(1, 1/3) + 10 Psi(1, 2/3) + Psi(1, 7/12) - Psi(1, ----)
12
________________________________________________
11
- 4 Psi(1, 5/6) + Psi(1, 5/12) + Psi(1, ----)
12
________________________________________________
11
- Psi(1, 1/4) + 9 Psi(1, 3/4) - Psi(1, 7/12) - Psi(1, ----)
12
________________________________________________
15 Psi(1, 2/3) - Psi(1, 1/6) - 4 Psi(1, 5/6)
________________________________________________
2 11
2 Pi - 10 Psi(1, 3/4) + Psi(1, 7/12) + Psi(1, ----)
12
________________________________________________
- 15 Psi(1, 1/3) + 4 Psi(1, 1/6) + Psi(1, 5/6)
________________________________________________
15 Psi(1, 1/3) - Psi(1, 5/6) - Psi(1, 1/12) - Psi(1, 7/12)
________________________________________________
2
- 4 Pi + 3 Psi(1, 1/3) + 3 Psi(1, 2/3)
________________________________________________
2 1/2
4 Pi 2 + 4 Psi(1, 1/4) - 2 Psi(1, 1/8) + Psi(1, 3/8) - Psi(1, 7/8)
________________________________________________
- Psi(1, 1/3) + 4 Psi(1, 2/3) - Psi(1, 5/6)
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
4 Psi(1, 3/4) - Psi(1, 3/8) - Psi(1, 7/8)
________________________________________________
- 4 Psi(1, 1/3) + Psi(1, 2/3) + Psi(1, 1/6)
________________________________________________
2
- 8 Pi + 4 Psi(1, 3/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
2 1/2
20 Pi 3 + 240 Psi(1, 2/3) - 120 Psi(1, 1/4) + 7 Psi(1, 1/12)
11
- 17 Psi(1, ----)
12
________________________________________________
2 2 1/2
- 4 Pi - 2 Pi 2 + Psi(1, 1/8) + Psi(1, 7/8)
________________________________________________
2 1/2
- 8 Pi 2 + 4 Psi(1, 5/6) - 4 Psi(1, 3/8) - 4 Psi(1, 5/8) + Psi(1, 1/12)
+ Psi(1, 7/12)
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
- 9 Psi(1, 1/4) + Psi(1, 3/4) + Psi(1, 1/12) + Psi(1, 5/12)
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
2
- 4 Pi + Psi(1, 1/6) + Psi(1, 5/6)
________________________________________________
2
- 4 Pi + Psi(1, 1/6) + Psi(1, 5/6)
________________________________________________
2
- 10 Pi + 60 Psi(1, 1/3) - 30 Psi(1, 1/4) + 3 Psi(1, 5/12) - 3 Psi(1, 7/12)
________________________________________________
2
- 8 Pi + Psi(1, 1/12) + Psi(1, 5/12) - 80 Catalan
________________________________________________
Psi(1, 1/3) - 4 Psi(1, 2/3) + Psi(1, 5/6)
________________________________________________
- 3 Psi(1, 1/3) - 3 Psi(1, 2/3) + 2 Psi(1, 1/4) + 2 Psi(1, 3/4)
________________________________________________
2 1/2
- 5 Psi(1, 1/4) - 5 Psi(1, 3/4) + 5 Psi(1, 1/5) + 5 Psi(1, 4/5) - 2 Pi 5
________________________________________________
2
4 Pi - Psi(1, 1/5) - Psi(1, 2/5) - Psi(1, 3/5) - Psi(1, 4/5)
________________________________________________
Psi(1, 1/3) - 4 Psi(1, 2/3) + Psi(1, 5/6)
________________________________________________
15 Psi(1, 2/3) + 10 Psi(1, 1/5) + 10 Psi(1, 4/5) - 6 Psi(1, 1/6)
2 1/2
- 9 Psi(1, 5/6) - 4 Pi 5
________________________________________________
15 Psi(1, 1/3) - 80 Psi(1, 1/4) + 3 Psi(1, 5/6) + 8 Psi(1, 1/12)
+ 8 Psi(1, 5/12)
________________________________________________
2 1/2
- 20 Pi 3 + 20 Psi(1, 1/5) + 20 Psi(1, 4/5) - 5 Psi(1, 5/12)
2 1/2
- 5 Psi(1, 7/12) - 8 Pi 5
________________________________________________
2
4 Pi - Psi(1, 1/6) - Psi(1, 5/6)
________________________________________________
2
2 Pi - Psi(1, 1/4) - Psi(1, 3/4)
________________________________________________
- 15 Psi(1, 1/3) + 16 Psi(1, 1/4) - 3 Psi(1, 5/6) - 128 Catalan
________________________________________________
2 2 1/2
- 10 Pi + 5 Psi(1, 2/5) + 5 Psi(1, 3/5) + 2 Pi 5
________________________________________________
2 1/2
36 Pi 3 - 40 Psi(1, 3/4) - 4 Psi(1, 1/12) + 5 Psi(1, 5/12)
+ 9 Psi(1, 7/12)
________________________________________________
Psi(1, 1/3) - 4 Psi(1, 2/3) + Psi(1, 5/6)
________________________________________________
2
- Pi + Psi(1, 1/4) - 8 Catalan
________________________________________________
2 1/2 11
- 2 Pi 3 - 8 Psi(1, 3/4) + 2 Psi(1, 1/6) + Psi(1, ----) - 24 Catalan
12
________________________________________________
- 8 Psi(1, 3/4) + Psi(1, 1/12) + Psi(1, 5/12) - 144 Catalan
________________________________________________
2
- 16 Pi + 15 Psi(1, 2/3) + 3 Psi(1, 1/6)
________________________________________________
15 Psi(1, 2/3) - Psi(1, 1/6) - 4 Psi(1, 5/6)
________________________________________________
- 60 Psi(1, 2/3) + 16 Psi(1, 5/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
11
60 Psi(1, 1/3) - 4 Psi(1, 1/12) - Psi(1, 5/12) - 4 Psi(1, 7/12) - Psi(1, ----)
12
________________________________________________
2 1/2
- 6 Pi 3 - 30 Psi(1, 1/3) + 4 Psi(1, 1/12) + Psi(1, 5/12) - 200 Catalan
________________________________________________
4 Psi(1, 1/4) - Psi(1, 1/8) - Psi(1, 5/8)
________________________________________________
- 4 Psi(1, 1/3) + Psi(1, 2/3) + Psi(1, 1/6)
________________________________________________
2 1/2
18 Pi 2 - 16 Psi(1, 3/4) - 9 Psi(1, 1/8) + 9 Psi(1, 3/8) + 2 Psi(1, 1/12)
+ 2 Psi(1, 5/12)
________________________________________________
2 1/2 2
2 Pi 3 - 5 Pi + 5 Psi(1, 3/4) - 2 Psi(1, 5/6) + Psi(1, 5/12)
________________________________________________
2
4 Pi - Psi(1, 1/8) - Psi(1, 5/8) + 32 Catalan
________________________________________________
2 1/2
- 32 Pi 3 - 75 Psi(1, 2/3) + 80 Psi(1, 3/4) + 17 Psi(1, 1/6)
- 16 Psi(1, 7/12)
________________________________________________
4 Psi(1, 1/4) - 2 Psi(1, 1/6) - 2 Psi(1, 5/6) + Psi(1, 3/8) + Psi(1, 7/8)
________________________________________________
2
Pi - Psi(1, 3/4) - 8 Catalan
________________________________________________
15 Psi(1, 1/3) + 35 Psi(1, 5/6) - 20 Psi(1, 1/8) - 20 Psi(1, 5/8)
11
+ 8 Psi(1, 1/12) - 8 Psi(1, ----)
12
________________________________________________
2 1/2 2
- 4 Pi 3 + 8 Pi - Psi(1, 5/12) - Psi(1, 7/12)
________________________________________________
2
- Pi + Psi(1, 1/4) - 8 Catalan
________________________________________________
2
- 4 Pi + Psi(1, 1/6) + Psi(1, 5/6)
________________________________________________
2
4 Pi - 15 Psi(1, 1/3) + 3 Psi(1, 1/6)
________________________________________________
- 4 Psi(1, 3/4) + Psi(1, 3/8) + Psi(1, 7/8)
________________________________________________
11
8 Psi(1, 1/4) - Psi(1, 7/12) - Psi(1, ----) - 144 Catalan
12
________________________________________________
2 1/2 11
2 Pi 3 + 2 Psi(1, 5/6) - Psi(1, ----) - 40 Catalan
12
________________________________________________
3 Psi(1, 1/3) + 3 Psi(1, 2/3) - 4 Psi(1, 3/4) - 32 Catalan
________________________________________________
- 3 Psi(1, 1/3) - 3 Psi(1, 2/3) + 4 Psi(1, 3/4) + 32 Catalan
________________________________________________
- Psi(1, 1/3) + 4 Psi(1, 2/3) - Psi(1, 5/6)
________________________________________________
4 Psi(1, 3/4) - Psi(1, 3/8) - Psi(1, 7/8)
________________________________________________
2 1/2
2 Pi 3 + 2 Psi(1, 1/6) - Psi(1, 1/12) + 40 Catalan
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
2 1/2
- 2 Pi 2 - 15 Psi(1, 2/3) + 3 Psi(1, 5/6) + Psi(1, 1/8) + Psi(1, 7/8)
________________________________________________
2 11
70 Pi - 60 Psi(1, 1/3) - 30 Psi(1, 1/4) + 3 Psi(1, 1/12) - 3 Psi(1, ----)
12
________________________________________________
2
16 Pi - 15 Psi(1, 2/3) - 3 Psi(1, 1/6)
________________________________________________
2 1/2
- 8 Pi 3 - 75 Psi(1, 1/3) + 20 Psi(1, 3/4) + 7 Psi(1, 1/6)
+ 4 Psi(1, 1/12)
________________________________________________
2 1/2
- 12 Pi 3 - 60 Psi(1, 1/3) - 7 Psi(1, 1/4) + 23 Psi(1, 3/4)
+ 6 Psi(1, 1/12)
________________________________________________
11
- 4 Psi(1, 5/6) + Psi(1, 5/12) + Psi(1, ----)
12
________________________________________________
- Psi(1, 1/4) + Psi(1, 3/4) + 16 Catalan
________________________________________________
2
Pi - Psi(1, 1/4) + 8 Catalan
________________________________________________
2 2 1/2
4 Pi + 2 Pi 2 - Psi(1, 1/8) - Psi(1, 7/8)
________________________________________________
- 15 Psi(1, 1/3) + 16 Psi(1, 3/4) - 3 Psi(1, 5/6) + 128 Catalan
________________________________________________
11
- 8 Psi(1, 3/4) + Psi(1, 7/12) + Psi(1, ----) + 16 Catalan
12
________________________________________________
- 15 Psi(1, 1/3) + 16 Psi(1, 1/4) - 3 Psi(1, 5/6) - 128 Catalan
________________________________________________
2
- 16 Pi + 15 Psi(1, 2/3) + 3 Psi(1, 1/6)
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
- 4 Psi(1, 1/3) + Psi(1, 2/3) + Psi(1, 1/6)
________________________________________________
2
Pi - Psi(1, 3/4) - 8 Catalan
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
- 4 Psi(1, 3/4) + Psi(1, 3/8) + Psi(1, 7/8)
________________________________________________
2 1/2 11
- 4 Pi 3 + 10 Psi(1, 1/3) - 10 Psi(1, 2/3) - Psi(1, 7/12) + Psi(1, ----)
12
________________________________________________
2
4 Pi - Psi(1, 1/6) - Psi(1, 5/6)
________________________________________________
2
- 18 Pi + 10 Psi(1, 3/4) + Psi(1, 1/12) + Psi(1, 5/12)
________________________________________________
15 Psi(1, 1/3) - 4 Psi(1, 1/6) - Psi(1, 5/6)
________________________________________________
2
- 4 Pi + Psi(1, 1/5) + Psi(1, 2/5) + Psi(1, 3/5) + Psi(1, 4/5)
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
2 1/2
- 4 Pi 3 - 40 Psi(1, 1/4) + 4 Psi(1, 5/6) + 5 Psi(1, 1/12)
+ 3 Psi(1, 5/12)
________________________________________________
2 1/2
- 2 Pi 3 + 2 Psi(1, 1/6) - Psi(1, 7/12) - 40 Catalan
________________________________________________
2
Pi - Psi(1, 1/4) + 8 Catalan
________________________________________________
2
- 16 Pi + 15 Psi(1, 1/3) + 3 Psi(1, 5/6)
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
2 1/2
4 Pi 3 - 6 Psi(1, 1/3) - 6 Psi(1, 2/3) + Psi(1, 5/12) + Psi(1, 7/12)
________________________________________________
Psi(1, 1/3) - 4 Psi(1, 2/3) + Psi(1, 5/6)
________________________________________________
2 1/2
2 Pi 3 + 2 Psi(1, 1/6) - Psi(1, 1/12) + 40 Catalan
________________________________________________
15 Psi(1, 1/3) - 20 Psi(1, 3/4) + 5 Psi(1, 1/6) - 2 Psi(1, 1/12)
11
+ 2 Psi(1, ----)
12
________________________________________________
- 240 Psi(1, 1/3) + 140 Psi(1, 1/4) + 5 Psi(1, 3/8) + 5 Psi(1, 7/8)
- 12 Psi(1, 5/12) + 12 Psi(1, 7/12)
________________________________________________
11
- 15 Psi(1, 2/3) + Psi(1, 1/6) + Psi(1, 5/12) + Psi(1, ----)
12
________________________________________________
Psi(1, 1/3) - 4 Psi(1, 2/3) + Psi(1, 5/6)
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
2
- 4 Pi + Psi(1, 1/6) + Psi(1, 5/6)
________________________________________________
2 2 1/2
- 2 Pi + 2 Pi 2 - 6 Psi(1, 3/4) + Psi(1, 5/8) - Psi(1, 7/8)
11
+ Psi(1, 7/12) + Psi(1, ----)
12
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 3/8) + Psi(1, 7/8) + 64 Catalan
________________________________________________
2
- 2 Pi + Psi(1, 1/4) + Psi(1, 3/4)
________________________________________________
2 1/2
- 48 Pi 3 - 240 Psi(1, 2/3) - 28 Psi(1, 3/4) + 23 Psi(1, 1/8)
11
+ 23 Psi(1, 5/8) + 24 Psi(1, ----)
12
________________________________________________
- 4 Psi(1, 1/3) + Psi(1, 2/3) + Psi(1, 1/6)
________________________________________________
11
- 4 Psi(1, 5/6) + Psi(1, 5/12) + Psi(1, ----)
12
________________________________________________
4 Psi(1, 3/4) - Psi(1, 1/8) - Psi(1, 5/8) + 64 Catalan
________________________________________________
2 2 1/2
- 4 Pi + 2 Pi 2 + 4 Psi(1, 1/4) - Psi(1, 1/8) + Psi(1, 3/8)
________________________________________________
2
- 4 Pi + 4 Psi(1, 1/3) - Psi(1, 2/3) + Psi(1, 5/6)
________________________________________________
- 4 Psi(1, 1/3) + Psi(1, 2/3) + Psi(1, 1/6)
________________________________________________
- 50 Psi(1, 1/4) + 5 Psi(1, 1/5) + 5 Psi(1, 4/5) + 5 Psi(1, 1/12)
2 1/2
+ 5 Psi(1, 5/12) - 2 Pi 5
________________________________________________
2
4 Pi - 15 Psi(1, 2/3) + 3 Psi(1, 5/6)
________________________________________________
2 1/2
- 28 Pi 3 + 60 Psi(1, 1/3) - 40 Psi(1, 1/4) + 4 Psi(1, 1/12)
11
- 7 Psi(1, 7/12) + 3 Psi(1, ----)
12
________________________________________________
- Psi(1, 1/4) + Psi(1, 3/4) + 16 Catalan
________________________________________________
2
- 4 Pi + 3 Psi(1, 1/3) + 3 Psi(1, 2/3)
________________________________________________
- 4 Psi(1, 1/3) + Psi(1, 2/3) + Psi(1, 1/6)
________________________________________________
2 2 1/2
16 Pi - 10 Pi 2 - 5 Psi(1, 5/8) + 5 Psi(1, 7/8) - 2 Psi(1, 7/12)
11
- 2 Psi(1, ----)
12
________________________________________________
2 1/2
- 6 Pi 3 + 15 Psi(1, 1/3) - 16 Psi(1, 3/4) + 9 Psi(1, 5/6)
- 3 Psi(1, 5/12) - 8 Catalan
________________________________________________
2
- 4 Pi + Psi(1, 1/6) + Psi(1, 5/6)
________________________________________________
2
- 4 Pi + Psi(1, 1/6) + Psi(1, 5/6)
________________________________________________
4 Psi(1, 1/4) - Psi(1, 1/6) - Psi(1, 5/6) - 32 Catalan
________________________________________________
2 1/2 2
- 8 Pi 3 + 20 Pi + 8 Psi(1, 5/6) - 5 Psi(1, 3/8) - 5 Psi(1, 7/8)
- 4 Psi(1, 5/12)
________________________________________________
Psi(1, 1/4) - 9 Psi(1, 3/4) + 4 Psi(1, 5/6) - Psi(1, 5/12) + Psi(1, 7/12)
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
- 4 Psi(1, 3/4) + Psi(1, 3/8) + Psi(1, 7/8)
________________________________________________
2 11
- 16 Pi + 30 Psi(1, 2/3) + 2 Psi(1, 1/6) - Psi(1, 5/12) - Psi(1, ----)
12
________________________________________________
2 11
18 Pi - 10 Psi(1, 1/4) - 4 Psi(1, 1/6) + Psi(1, 1/12) - Psi(1, ----)
12
________________________________________________
- 16 Psi(1, 1/3) + 4 Psi(1, 2/3) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
2
- Pi + Psi(1, 3/4) + 8 Catalan
________________________________________________
- 15 Psi(1, 2/3) + 3 Psi(1, 5/6) + Psi(1, 3/8) + Psi(1, 7/8) + 32 Catalan
________________________________________________
11
8 Psi(1, 1/4) - Psi(1, 7/12) - Psi(1, ----) - 144 Catalan
12
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
4 Psi(1, 1/3) - Psi(1, 2/3) - Psi(1, 1/6)
________________________________________________
2
2 Pi + 15 Psi(1, 1/3) + 6 Psi(1, 3/4) - 3 Psi(1, 1/6) - Psi(1, 1/8)
11
- Psi(1, 5/8) - Psi(1, 7/12) - Psi(1, ----)
12
________________________________________________
11
Psi(1, 1/4) - 9 Psi(1, 3/4) + Psi(1, 7/12) + Psi(1, ----)
12
________________________________________________
2
40 Pi - 60 Psi(1, 2/3) + 3 Psi(1, 5/12) - 3 Psi(1, 7/12) - 240 Catalan
________________________________________________
2 1/2
- 4 Pi 3 - 4 Psi(1, 3/4) - Psi(1, 1/8) - Psi(1, 5/8) + Psi(1, 1/12)
11
+ Psi(1, ----)
12
________________________________________________
Psi(1, 1/3) - 4 Psi(1, 2/3) + Psi(1, 5/6)
________________________________________________
540 Psi(1, 1/3) - 320 Psi(1, 1/4) + 27 Psi(1, 5/12) - 32 Psi(1, 7/12)
11
- 5 Psi(1, ----)
12
________________________________________________
- 3 Psi(1, 1/3) - 3 Psi(1, 2/3) + 4 Psi(1, 3/4) + 32 Catalan
________________________________________________
- 4 Psi(1, 1/3) + Psi(1, 2/3) + Psi(1, 1/6)
________________________________________________
2 1/2
8 Pi 2 + 15 Psi(1, 2/3) + 3 Psi(1, 1/6) - 4 Psi(1, 1/8) - 4 Psi(1, 7/8)
________________________________________________
2
- 4 Pi + 15 Psi(1, 1/3) - 3 Psi(1, 1/6)
________________________________________________
2 1/2
- 2 Pi 3 + 2 Psi(1, 5/6) - Psi(1, 5/12) + 40 Catalan
________________________________________________
- 15 Psi(1, 2/3) + 5 Psi(1, 1/6) + 2 Psi(1, 5/12) - 2 Psi(1, 7/12)
- 160 Catalan
________________________________________________
2 1/2
- 4 Pi 2 + 4 Psi(1, 1/4) - Psi(1, 3/8) - 2 Psi(1, 5/8) + Psi(1, 7/8)
________________________________________________
135 Psi(1, 2/3) - 80 Psi(1, 1/4) + 27 Psi(1, 1/6) - 8 Psi(1, 7/12)
11
- 8 Psi(1, ----)
12
________________________________________________
2
- 2 Pi + Psi(1, 1/4) + Psi(1, 3/4)
________________________________________________
15 Psi(1, 1/3) - 4 Psi(1, 1/6) - Psi(1, 5/6)
________________________________________________
2
Pi - Psi(1, 3/4) - 8 Catalan
________________________________________________
2 11
- 16 Pi + 4 Psi(1, 1/6) + Psi(1, 5/12) + Psi(1, ----)
12
________________________________________________
11
- 4 Psi(1, 5/6) + Psi(1, 5/12) + Psi(1, ----)
12
________________________________________________
- 135 Psi(1, 2/3) + 20 Psi(1, 3/4) + 27 Psi(1, 5/6) + 2 Psi(1, 1/12)
+ 2 Psi(1, 5/12)
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
- 15 Psi(1, 1/3) + 16 Psi(1, 3/4) - 3 Psi(1, 5/6) + 128 Catalan
________________________________________________
- 16 Psi(1, 1/3) + 4 Psi(1, 2/3) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
2
Pi - Psi(1, 1/4) + 8 Catalan
________________________________________________
15 Psi(1, 1/3) - 80 Psi(1, 1/4) + 3 Psi(1, 5/6) + 8 Psi(1, 1/12)
+ 8 Psi(1, 5/12)
________________________________________________
2
4 Pi - 15 Psi(1, 2/3) + 3 Psi(1, 5/6)
________________________________________________
- 4 Psi(1, 3/4) + Psi(1, 3/8) + Psi(1, 7/8)
________________________________________________
- 4 Psi(1, 3/4) + Psi(1, 3/8) + Psi(1, 7/8)
________________________________________________
2 11
16 Pi - 60 Psi(1, 2/3) + 3 Psi(1, 5/12) + 3 Psi(1, ----)
12
________________________________________________
Psi(1, 1/3) - 4 Psi(1, 2/3) + Psi(1, 5/6)
________________________________________________
4 Psi(1, 1/4) - Psi(1, 3/8) - Psi(1, 7/8) - 64 Catalan
________________________________________________
2 1/2 2 11
- 4 Pi 3 - 8 Pi + Psi(1, 1/12) + Psi(1, ----)
12
________________________________________________
2 1/2
- 32 Pi 3 - 45 Psi(1, 2/3) - 80 Psi(1, 3/4) + 23 Psi(1, 1/6)
11
+ 16 Psi(1, ----)
12
________________________________________________
2 1/2
- 8 Pi 3 - 23 Psi(1, 1/3) + 17 Psi(1, 2/3) + 20 Psi(1, 1/4)
- 4 Psi(1, 5/12)
________________________________________________
- 4 Psi(1, 3/4) + Psi(1, 3/8) + Psi(1, 7/8)
________________________________________________
2 1/2
- 8 Pi 2 - 15 Psi(1, 1/3) - 3 Psi(1, 5/6) + 4 Psi(1, 1/8) + 4 Psi(1, 7/8)
________________________________________________
2
- 16 Pi + 4 Psi(1, 5/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
2 1/2 2
4 Pi 3 - 8 Pi + Psi(1, 5/12) + Psi(1, 7/12)
________________________________________________
Psi(1, 1/4) - Psi(1, 3/4) - 16 Catalan
________________________________________________
2
16 Pi - 15 Psi(1, 2/3) - 3 Psi(1, 1/6)
________________________________________________
- 4 Psi(1, 1/3) + Psi(1, 2/3) + Psi(1, 1/6)
________________________________________________
2 1/2
8 Pi 2 - 15 Psi(1, 2/3) - 3 Psi(1, 1/6) + 4 Psi(1, 3/8) + 4 Psi(1, 5/8)
________________________________________________
2
40 Pi - 60 Psi(1, 1/3) - 3 Psi(1, 5/12) + 3 Psi(1, 7/12) + 240 Catalan
________________________________________________
- 15 Psi(1, 1/3) - 3 Psi(1, 5/6) + 4 Psi(1, 1/8) + 4 Psi(1, 5/8) - 128 Catalan
________________________________________________
2
Pi - Psi(1, 3/4) - 8 Catalan
________________________________________________
2 1/2
2 Pi 2 - Psi(1, 1/8) + Psi(1, 3/8) + 32 Catalan
________________________________________________
- 15 Psi(1, 2/3) + Psi(1, 1/6) + 4 Psi(1, 5/6)
________________________________________________
2
- 4 Pi + 15 Psi(1, 1/3) - 3 Psi(1, 1/6)
________________________________________________
11
- 60 Psi(1, 2/3) + 2 Psi(1, 1/12) + 5 Psi(1, 5/12) + 3 Psi(1, ----)
12
- 160 Catalan
________________________________________________
2
4 Pi - 3 Psi(1, 1/3) - 3 Psi(1, 2/3)
________________________________________________
2
- 2 Pi + Psi(1, 1/4) + Psi(1, 3/4)
________________________________________________
- 3 Psi(1, 1/3) - 3 Psi(1, 2/3) + 2 Psi(1, 1/4) + 2 Psi(1, 3/4)
________________________________________________
2 11
2 Pi - 10 Psi(1, 3/4) + Psi(1, 7/12) + Psi(1, ----)
12
________________________________________________
2 11
16 Pi - 60 Psi(1, 2/3) + 3 Psi(1, 5/12) + 3 Psi(1, ----)
12
________________________________________________
2 1/2
- 4 Pi 3 - 4 Psi(1, 1/4) - Psi(1, 3/8) - Psi(1, 7/8) + Psi(1, 1/12)
11
+ Psi(1, ----)
12
________________________________________________
50 Psi(1, 3/4) - 5 Psi(1, 1/5) - 5 Psi(1, 4/5) - 5 Psi(1, 7/12)
11 2 1/2
- 5 Psi(1, ----) + 2 Pi 5
12
________________________________________________
2
18 Pi - 10 Psi(1, 3/4) - Psi(1, 1/12) - Psi(1, 5/12)
________________________________________________
2
16 Pi - 15 Psi(1, 1/3) - 3 Psi(1, 5/6)
________________________________________________
- 30 Psi(1, 1/3) + 10 Psi(1, 1/6) + Psi(1, 5/12) - Psi(1, 7/12) - 80 Catalan
________________________________________________
2
- 16 Pi + 15 Psi(1, 2/3) + 3 Psi(1, 1/6)
________________________________________________
Psi(1, 1/3) - 4 Psi(1, 2/3) + Psi(1, 5/6)
________________________________________________
2 1/2
4 Pi 3 - Psi(1, 1/12) + Psi(1, 7/12) + 80 Catalan
________________________________________________
Psi(1, 1/4) - Psi(1, 3/4) - 16 Catalan
________________________________________________
30 Psi(1, 2/3) - 10 Psi(1, 5/6) + Psi(1, 5/12) - Psi(1, 7/12) - 80 Catalan
________________________________________________
2 1/2
- 6 Pi 3 + 30 Psi(1, 2/3) - 8 Psi(1, 3/4) - 3 Psi(1, 5/12) + 56 Catalan
________________________________________________
2
16 Pi - 15 Psi(1, 1/3) - 3 Psi(1, 5/6)
________________________________________________
2 1/2
6 Pi 3 - 30 Psi(1, 2/3) + 8 Psi(1, 3/4) + 3 Psi(1, 5/12) - 56 Catalan
________________________________________________
2
8 Pi - 4 Psi(1, 1/4) - Psi(1, 3/8) - Psi(1, 7/8)
________________________________________________
- 15 Psi(1, 1/3) + 16 Psi(1, 1/4) - 3 Psi(1, 5/6) - 128 Catalan
________________________________________________
11
- 4 Psi(1, 1/3) + 16 Psi(1, 2/3) - Psi(1, 5/12) - Psi(1, ----)
12
________________________________________________
2 1/2 2 11
- 2 Pi 3 - 13 Pi + 5 Psi(1, 1/4) + 2 Psi(1, 1/6) + Psi(1, ----)
12
________________________________________________
11
- 4 Psi(1, 5/6) + Psi(1, 5/12) + Psi(1, ----)
12
________________________________________________
2 2 1/2
10 Pi - 5 Psi(1, 2/5) - 5 Psi(1, 3/5) - 2 Pi 5
________________________________________________
2
16 Pi - 15 Psi(1, 2/3) - 3 Psi(1, 1/6)
________________________________________________
4 Psi(1, 1/3) - Psi(1, 2/3) - Psi(1, 1/6)
________________________________________________
2
Pi - Psi(1, 1/4) + 8 Catalan
________________________________________________
3 Psi(1, 1/3) + 3 Psi(1, 2/3) - 2 Psi(1, 1/4) - 2 Psi(1, 3/4)
________________________________________________
- 4 Psi(1, 3/4) + Psi(1, 3/8) + Psi(1, 7/8)
________________________________________________
15 Psi(1, 1/3) - Psi(1, 1/5) - Psi(1, 2/5) - Psi(1, 3/5) - Psi(1, 4/5)
- 3 Psi(1, 1/6)
________________________________________________
2 1/2 2
- 2 Pi 3 + 13 Pi - 5 Psi(1, 3/4) - 2 Psi(1, 1/6) - Psi(1, 5/12)
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
2 1/2
15 Psi(1, 1/3) + 15 Psi(1, 2/3) - 10 Psi(1, 2/5) - 10 Psi(1, 3/5) - 4 Pi 5
________________________________________________
15 Psi(1, 1/3) - 4 Psi(1, 1/6) - Psi(1, 5/6)
________________________________________________
2
- 70 Pi + 60 Psi(1, 1/3) + 30 Psi(1, 3/4) + 3 Psi(1, 5/12) - 3 Psi(1, 7/12)
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
- 5 Psi(1, 1/3) + 35 Psi(1, 2/3) - 4 Psi(1, 1/4) - 2 Psi(1, 5/12)
11
- 2 Psi(1, ----) + 32 Catalan
12
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
2 1/2
- 8 Pi 3 + 15 Psi(1, 1/3) + 3 Psi(1, 5/6) - 2 Psi(1, 5/12)
- 2 Psi(1, 7/12)
________________________________________________
15 Psi(1, 2/3) - 4 Psi(1, 3/4) - 3 Psi(1, 5/6) - 32 Catalan
________________________________________________
2
4 Pi - Psi(1, 1/6) - Psi(1, 5/6)
________________________________________________
- Psi(1, 1/3) + 4 Psi(1, 2/3) - Psi(1, 5/6)
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
2 1/2
- 2 Pi 2 - 28 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 7/8) + 3 Psi(1, 1/12)
+ 3 Psi(1, 5/12) - 16 Catalan
________________________________________________
- 15 Psi(1, 1/3) + 4 Psi(1, 1/6) + Psi(1, 5/6)
________________________________________________
2
- Pi + Psi(1, 1/4) - 8 Catalan
________________________________________________
- 5 Psi(1, 1/3) + 35 Psi(1, 2/3) - 20 Psi(1, 1/4) + 2 Psi(1, 1/12)
11
- 2 Psi(1, ----)
12
________________________________________________
- 20 Psi(1, 1/4) + Psi(1, 1/5) + Psi(1, 2/5) + Psi(1, 3/5) + Psi(1, 4/5)
+ 2 Psi(1, 1/12) + 2 Psi(1, 5/12)
________________________________________________
2
- 2 Pi + Psi(1, 1/4) + Psi(1, 3/4)
________________________________________________
2
4 Pi - 3 Psi(1, 1/3) - 3 Psi(1, 2/3)
________________________________________________
- 20 Psi(1, 3/4) + Psi(1, 1/6) + 9 Psi(1, 5/6) - 2 Psi(1, 5/12)
+ 2 Psi(1, 7/12)
________________________________________________
2 1/2
2 Pi 3 - 2 Psi(1, 1/6) + Psi(1, 7/12) + 40 Catalan
________________________________________________
15 Psi(1, 2/3) - Psi(1, 1/6) - 4 Psi(1, 5/6)
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
2
- 16 Pi + 15 Psi(1, 2/3) + 3 Psi(1, 1/6)
________________________________________________
15 Psi(1, 1/3) - 4 Psi(1, 1/6) - Psi(1, 5/6)
________________________________________________
2 1/2
- 8 Pi 3 - 45 Psi(1, 1/3) + 16 Psi(1, 3/4) - Psi(1, 5/6) + 4 Psi(1, 1/12)
- 32 Catalan
________________________________________________
- 16 Psi(1, 1/3) + 4 Psi(1, 2/3) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
- 15 Psi(1, 1/3) + 8 Psi(1, 1/4) - 3 Psi(1, 5/6) + 2 Psi(1, 3/8)
+ 2 Psi(1, 7/8)
________________________________________________
2
- 2 Pi + Psi(1, 1/4) + Psi(1, 3/4)
________________________________________________
11
- Psi(1, 1/4) + 9 Psi(1, 3/4) - Psi(1, 7/12) - Psi(1, ----)
12
________________________________________________
2 1/2
- 2 Pi 3 + 2 Psi(1, 5/6) - Psi(1, 5/12) + 40 Catalan
________________________________________________
2 1/2 2
6 Pi 3 - 32 Pi + 30 Psi(1, 1/3) + 3 Psi(1, 5/12) - 120 Catalan
________________________________________________
- 4 Psi(1, 1/4) + Psi(1, 1/8) + Psi(1, 5/8)
________________________________________________
2
- 16 Pi + 15 Psi(1, 1/3) + 3 Psi(1, 5/6)
________________________________________________
- 15 Psi(1, 1/3) + 4 Psi(1, 1/4) + 3 Psi(1, 1/6) - 32 Catalan
________________________________________________
- 4 Psi(1, 1/6) + Psi(1, 1/12) + Psi(1, 7/12)
________________________________________________