-
- A few identities
(IV)
- with Zeta(3)
- 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
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________________________________
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 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)
_______________________________________________________________________
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
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
_______________________________________________________________________
- 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)
_______________________________________________________________________
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
_______________________________________________________________________
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)
_______________________________________________________________________
- 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)
_______________________________________________________________________
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)
_______________________________________________________________________
- 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)
_______________________________________________________________________
- 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
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)
_______________________________________________________________________
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)
_______________________________________________________________________
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)
_______________________________________________________________________
- 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)
_______________________________________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________________________________
3
2 Pi - 56 Zeta(3) - Psi(2, 3/4)
_______________________________________________________________________
- 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 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)
_______________________________________________________________________
11
- 3328 Zeta(3) - 72 Psi(2, 1/3) - Psi(2, 5/12) - Psi(2, ----)
12
_______________________________________________________________________
- 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 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
_______________________________________________________________________
- 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)
_______________________________________________________________________
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)
_______________________________________________________________________
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, 1/6)
_______________________________________________________________________
- 112 Zeta(3) - Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________________________________
- Psi(2, 1/3) + 8 Psi(2, 2/3) - Psi(2, 5/6)
_______________________________________________________________________
- 112 Zeta(3) - Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________________________________
- 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)
_______________________________________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________________________________
3
2 Pi - 56 Zeta(3) - Psi(2, 3/4)
_______________________________________________________________________
364 Zeta(3) + Psi(2, 1/6) + Psi(2, 5/6)
_______________________________________________________________________
3328 Zeta(3) + Psi(2, 1/12) + 72 Psi(2, 2/3) + 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 3 1/2
6 Pi + 12 Pi 3 - 14 Zeta(3) + 3 Psi(2, 1/4) + Psi(2, 1/6) - 2 Psi(2, 5/6)
_______________________________________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________________________________
- 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 11
64 Pi 3 + 504 Psi(2, 2/3) - 9 Psi(2, 5/12) - 9 Psi(2, ----)
12
_______________________________________________________________________
3
2 Pi + 56 Zeta(3) + Psi(2, 1/4)
_______________________________________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________________________________
3
56 Pi - 28 Psi(2, 1/3) + Psi(2, 1/12) - 28 Psi(2, 2/3) + Psi(2, 5/12)
_______________________________________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________________________________
3 1/2
- 8 Pi 3 - 63 Psi(2, 2/3) + 9 Psi(2, 5/6)
_______________________________________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________________________________
3
32 Pi + 8 Psi(2, 1/4) - Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________________________________
3 1/2
- 8 Pi 3 - 9 Psi(2, 1/3) + 9 Psi(2, 2/3)
_______________________________________________________________________
- 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)
_______________________________________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________________________________
Psi(2, 1/3) - 8 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________________________________
- 63 Psi(2, 1/3) + Psi(2, 1/12) + Psi(2, 5/6) + Psi(2, 7/12)
_______________________________________________________________________
3024 Zeta(3) + Psi(2, 1/12) + 28 Psi(2, 3/4) + Psi(2, 5/12)
_______________________________________________________________________
3 3 1/2
- 16 Pi - 8 Pi 3 + 20 Zeta(3) - Psi(2, 1/8) + 18 Psi(2, 2/3)
- Psi(2, 5/8)
_______________________________________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________________________________
3 1/2
64 Pi 3 + 9 Psi(2, 1/6) - 63 Psi(2, 2/3)
_______________________________________________________________________
3 1/2
- 8 Pi 3 - 52 Zeta(3) - 9 Psi(2, 1/3) + Psi(2, 5/6)
_______________________________________________________________________
11
112 Zeta(3) + 28 Psi(2, 3/4) - Psi(2, 7/12) - Psi(2, ----)
12
_______________________________________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________________________________
3
2 Pi + 56 Zeta(3) + Psi(2, 1/4)
_______________________________________________________________________
11
8 Psi(2, 5/6) - Psi(2, 5/12) - Psi(2, ----)
12
_______________________________________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________________________________
3 1/2
12 Pi 2 + 448 Zeta(3) + Psi(2, 1/8) + Psi(2, 3/8)
_______________________________________________________________________
3 11
- 56 Pi + 1872 Zeta(3) + 72 Psi(2, 1/3) - Psi(2, 1/12) + Psi(2, ----)
12
_______________________________________________________________________
8 Psi(2, 3/4) - Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________________________________
3 1/2
64 Pi 3 - 504 Psi(2, 1/3) + 9 Psi(2, 1/12) + 9 Psi(2, 7/12)
_______________________________________________________________________
3 3 1/2
26 Pi + 16 Pi 3 + 13 Psi(2, 1/4) - 4 Psi(2, 5/6)
_______________________________________________________________________
3 3 1/2
56 Pi - 32 Pi 3 + Psi(2, 5/12) - Psi(2, 7/12)
_______________________________________________________________________
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
2 Pi + 56 Zeta(3) + Psi(2, 1/4)
_______________________________________________________________________
28 Psi(2, 1/3) - 13 Psi(2, 1/4) + 28 Psi(2, 2/3) - 13 Psi(2, 3/4)
_______________________________________________________________________
- 52 Zeta(3) - Psi(2, 1/3) - Psi(2, 2/3)
_______________________________________________________________________
3
- 22 Pi + 63 Psi(2, 1/3) - 39 Psi(2, 1/4) + 2 Psi(2, 1/6) + 9 Psi(2, 5/6)
11
- Psi(2, 7/12) - Psi(2, ----)
12
_______________________________________________________________________
3 3 1/2
- 4 Pi - 4 Pi 3 + 10 Zeta(3) - 3 Psi(2, 1/4) + 9 Psi(2, 2/3)
- Psi(2, 3/4)
_______________________________________________________________________
3
4 Pi + Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________________________________
3
- 32 Pi - 8 Psi(2, 1/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________________________________
3 1/2
4 Pi 3 + 234 Zeta(3) + 9 Psi(2, 1/3)
_______________________________________________________________________
- 13 Psi(2, 1/4) + 4 Psi(2, 1/6) - 13 Psi(2, 3/4) + 4 Psi(2, 5/6)
_______________________________________________________________________
- 896 Zeta(3) - Psi(2, 1/8) - 8 Psi(2, 3/4) - Psi(2, 5/8)
_______________________________________________________________________
- 64 Zeta(3) + 18 Psi(2, 1/3) - Psi(2, 1/8) - 8 Psi(2, 3/4) + 2 Psi(2, 5/6)
- Psi(2, 5/8)
_______________________________________________________________________
3 3 1/2
26 Pi - 16 Pi 3 - 13 Psi(2, 3/4) + 4 Psi(2, 5/6)
_______________________________________________________________________
- 52 Zeta(3) - 9 Psi(2, 1/3) + Psi(2, 1/6)
_______________________________________________________________________
3 11
76 Pi + 504 Psi(2, 1/3) - 7 Psi(2, 1/12) - 234 Psi(2, 3/4) + 7 Psi(2, ----)
12
_______________________________________________________________________
3
2 Pi - 56 Zeta(3) - Psi(2, 3/4)
_______________________________________________________________________
- Psi(2, 1/12) + 504 Psi(2, 2/3) - 64 Psi(2, 5/6) - 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)
_______________________________________________________________________
3
- 2 Pi + 56 Zeta(3) + Psi(2, 3/4)
_______________________________________________________________________
8 Psi(2, 3/4) - Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________________________________
3
4 Pi + Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________________________________
3
8 Pi + 80 Zeta(3) + 72 Psi(2, 1/3) - Psi(2, 1/12) - 32 Psi(2, 3/4)
11
+ Psi(2, ----)
12
_______________________________________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________________________________
3 1/2 11
- 8 Pi 3 - Psi(2, 1/6) - 7 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________________________________
- 112 Zeta(3) - 28 Psi(2, 1/4) + 8 Psi(2, 1/6) + Psi(2, 5/12) - Psi(2, 7/12)
_______________________________________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________________________________
3 1/2
- 12 Pi 2 + 448 Zeta(3) + Psi(2, 5/8) + Psi(2, 7/8)
_______________________________________________________________________
3 1/2
8 Pi 3 - 63 Psi(2, 1/3) + 9 Psi(2, 1/6)
_______________________________________________________________________
3 11
102 Pi - 168 Zeta(3) + 23 Psi(2, 1/4) - Psi(2, 7/12) - Psi(2, ----)
12
_______________________________________________________________________
3
4 Pi + 26 Psi(2, 3/4) - 8 Psi(2, 5/6) + Psi(2, 5/12) - Psi(2, 7/12)
_______________________________________________________________________
3 1/2
- 8 Pi 3 + 63 Psi(2, 1/3) - 9 Psi(2, 1/6)
_______________________________________________________________________
11
- 3328 Zeta(3) - 72 Psi(2, 1/3) - Psi(2, 5/12) - Psi(2, ----)
12
_______________________________________________________________________
52 Zeta(3) + Psi(2, 1/3) + Psi(2, 2/3)
_______________________________________________________________________
3 1/2 11
64 Pi 3 + Psi(2, 1/12) - Psi(2, 5/12) + Psi(2, 7/12) - Psi(2, ----)
12
_______________________________________________________________________
3 1/2
12 Pi 2 + 448 Zeta(3) + Psi(2, 1/8) + Psi(2, 3/8)
_______________________________________________________________________
- 63 Psi(2, 1/3) + 26 Psi(2, 1/4) + 26 Psi(2, 3/4) - 7 Psi(2, 5/6)
_______________________________________________________________________
- 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, 3/8) + Psi(2, 5/8)
_______________________________________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________________________________
3
26 Pi + 126 Psi(2, 1/3) - 14 Psi(2, 1/6) - 13 Psi(2, 3/4)
_______________________________________________________________________
3 1/2
8 Pi 3 + Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________________________________
3 1/2
- 8 Pi 3 - 63 Psi(2, 2/3) + 9 Psi(2, 5/6)
_______________________________________________________________________
3 1/2
- 36 Pi 3 + 26 Zeta(3) - 5 Psi(2, 1/6) + 36 Psi(2, 2/3)
_______________________________________________________________________
3 3 1/2
- 6 Pi - 4 Pi 3 - 14 Zeta(3) - Psi(2, 1/6) + 3 Psi(2, 3/4)
_______________________________________________________________________
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)
_______________________________________________________________________
3 1/2
- 8 Pi 3 - 9 Psi(2, 1/3) + 9 Psi(2, 2/3)
_______________________________________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________________________________
- 416 Zeta(3) - 9 Psi(2, 1/3) - Psi(2, 5/6)
_______________________________________________________________________
Psi(2, 1/3) - 8 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________________________________
- 112 Zeta(3) - Psi(2, 1/6) + 63 Psi(2, 2/3) - 28 Psi(2, 3/4) - Psi(2, 5/12)
+ Psi(2, 7/12)
_______________________________________________________________________
- 8 Psi(2, 1/3) + Psi(2, 1/6) + Psi(2, 2/3)
_______________________________________________________________________
3 1/2
- 12 Pi 2 - 448 Zeta(3) - Psi(2, 1/8) - Psi(2, 3/8)
_______________________________________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________________________________
3 1/2
8 Pi 3 + 52 Zeta(3) + 9 Psi(2, 1/3) - Psi(2, 5/6)
_______________________________________________________________________
3 1/2
4 Pi 3 + 234 Zeta(3) + 9 Psi(2, 1/3)
_______________________________________________________________________
3 1/2
- 4 Pi 3 - 182 Zeta(3) - Psi(2, 1/6)
_______________________________________________________________________
3 1/2
8 Pi 3 + 9 Psi(2, 1/3) - 9 Psi(2, 2/3)
_______________________________________________________________________
3
- 26 Pi - 13 Psi(2, 1/4) + 126 Psi(2, 2/3) - 14 Psi(2, 5/6)
_______________________________________________________________________
Psi(2, 1/3) - 8 Psi(2, 2/3) + Psi(2, 5/6)
_______________________________________________________________________
- 27 Psi(2, 1/4) + Psi(2, 1/12) + Psi(2, 3/4) + Psi(2, 5/12)
_______________________________________________________________________
3 3 1/2
56 Pi - 32 Pi 3 + Psi(2, 5/12) - Psi(2, 7/12)
_______________________________________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________________________________
416 Zeta(3) + 72 Psi(2, 1/3) - Psi(2, 1/12) - Psi(2, 7/12)
_______________________________________________________________________
3
- 108 Pi - 8 Psi(2, 1/6) + 26 Psi(2, 3/4) - Psi(2, 5/12) + Psi(2, 7/12)
_______________________________________________________________________
52 Zeta(3) + 9 Psi(2, 1/3) - Psi(2, 1/6)
_______________________________________________________________________
3 1/2
8 Pi 3 + 9 Psi(2, 1/3) - 9 Psi(2, 2/3)
_______________________________________________________________________
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
4 Pi 3 - 234 Zeta(3) - 9 Psi(2, 2/3)
_______________________________________________________________________
3
2 Pi + 56 Zeta(3) + Psi(2, 1/4)
_______________________________________________________________________
13 Psi(2, 1/4) - 4 Psi(2, 1/6) + 13 Psi(2, 3/4) - 4 Psi(2, 5/6)
_______________________________________________________________________
3 11
112 Pi - 9 Psi(2, 1/6) + 2 Psi(2, 1/12) + 63 Psi(2, 2/3) - 2 Psi(2, ----)
12
_______________________________________________________________________
3 1/2
64 Pi 3 + 9 Psi(2, 1/6) - 63 Psi(2, 2/3)
_______________________________________________________________________
8 Psi(2, 3/4) - Psi(2, 3/8) - 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 - 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
- 4 Pi 3 - 234 Zeta(3) - 9 Psi(2, 1/3)
_______________________________________________________________________
3 1/2
8 Pi 3 + Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________________________________
3
2 Pi - 56 Zeta(3) - Psi(2, 3/4)
_______________________________________________________________________
- 416 Zeta(3) - Psi(2, 1/6) - 9 Psi(2, 2/3)
_______________________________________________________________________
- 416 Zeta(3) - Psi(2, 1/6) - 9 Psi(2, 2/3)
_______________________________________________________________________
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
4 Pi 3 - 234 Zeta(3) - 9 Psi(2, 2/3)
_______________________________________________________________________
3 1/2
4 Pi 3 + 26 Zeta(3) + 36 Psi(2, 2/3) - 5 Psi(2, 5/6)
_______________________________________________________________________
- 8 Psi(2, 1/3) + Psi(2, 1/6) + Psi(2, 2/3)
_______________________________________________________________________
11
416 Zeta(3) + 72 Psi(2, 2/3) - Psi(2, 5/12) - Psi(2, ----)
12
_______________________________________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________________________________
3
26 Pi + 13 Psi(2, 1/4) - 2 Psi(2, 1/6) - 2 Psi(2, 5/6)
_______________________________________________________________________
3 1/2 3 1/2
64 Pi 3 + 84 Pi 2 + 7 Psi(2, 1/8) - 2 Psi(2, 5/12) + 2 Psi(2, 7/12)
- 7 Psi(2, 7/8)
_______________________________________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________________________________
- 416 Zeta(3) - 9 Psi(2, 1/3) - Psi(2, 5/6)
_______________________________________________________________________
64 Psi(2, 1/6) - 27 Psi(2, 1/8) + 8 Psi(2, 3/4) + 8 Psi(2, 5/12)
- 8 Psi(2, 7/12) - 27 Psi(2, 5/8)
_______________________________________________________________________
11
- Psi(2, 1/6) + 63 Psi(2, 2/3) - Psi(2, 5/12) - Psi(2, ----)
12
_______________________________________________________________________
- 112 Zeta(3) - Psi(2, 1/4) - Psi(2, 3/4)
_______________________________________________________________________
3 1/2
8 Pi 3 - 63 Psi(2, 1/3) + 9 Psi(2, 1/6)
_______________________________________________________________________
3
- 26 Pi - 2 Psi(2, 1/6) + 13 Psi(2, 3/4) - 2 Psi(2, 5/6)
_______________________________________________________________________
3
- 4 Pi - Psi(2, 1/4) + Psi(2, 3/4)
_______________________________________________________________________
3 1/2
- 8 Pi 3 - 9 Psi(2, 1/3) + 9 Psi(2, 2/3)
_______________________________________________________________________
- 416 Zeta(3) - 9 Psi(2, 1/3) - Psi(2, 5/6)
_______________________________________________________________________
3 3 1/2
234 Pi + 112 Pi 3 + 117 Psi(2, 1/4) - 252 Psi(2, 2/3)
_______________________________________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________________________________
3 1/2
32 Pi 3 + 14 Psi(2, 1/4) - 14 Psi(2, 3/4) - Psi(2, 5/12) + Psi(2, 7/12)
_______________________________________________________________________
3 1/2
- 8 Pi 3 - 63 Psi(2, 2/3) + 9 Psi(2, 5/6)
_______________________________________________________________________
3
56 Pi + 1456 Zeta(3) + Psi(2, 1/12) + Psi(2, 5/12)
_______________________________________________________________________
3 1/2 3 1/2
- 72 Pi 3 + 84 Pi 2 + 7 Psi(2, 1/8) - 2 Psi(2, 1/12) - 63 Psi(2, 2/3)
11
+ 9 Psi(2, 5/6) + 2 Psi(2, ----) - 7 ps
12
_______________________________________________________________________
7/8
_______________________________________________________________________
3 1/2
8 Pi 3 - 12 Zeta(3) + 27 Psi(2, 1/3) - 8 Psi(2, 1/4) + Psi(2, 5/6)
- Psi(2, 3/8) - Psi(2, 7/8)
_______________________________________________________________________
3 11
112 Pi + Psi(2, 1/12) + Psi(2, 5/12) - Psi(2, 7/12) - Psi(2, ----)
12
_______________________________________________________________________
Psi(2, 1/6) - 63 Psi(2, 2/3) + 8 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 + Psi(2, 1/6) - Psi(2, 5/6)
_______________________________________________________________________
304 Zeta(3) + 72 Psi(2, 2/3) - 28 Psi(2, 3/4) - Psi(2, 5/12) + Psi(2, 7/12)
_______________________________________________________________________
3 1/2
4 Pi 3 - 182 Zeta(3) - Psi(2, 5/6)
_______________________________________________________________________
896 Zeta(3) + Psi(2, 1/8) + 8 Psi(2, 3/4) + Psi(2, 5/8)
_______________________________________________________________________
- 896 Zeta(3) - Psi(2, 1/8) - 8 Psi(2, 3/4) - Psi(2, 5/8)
_______________________________________________________________________
3 11
108 Pi + 26 Psi(2, 1/4) - Psi(2, 7/12) - Psi(2, ----)
12
_______________________________________________________________________
3 3 1/2
16 Pi - 12 Pi 2 - Psi(2, 3/8) + Psi(2, 5/8)
_______________________________________________________________________
3 1/2
- 64 Pi 3 - 9 Psi(2, 1/6) + 63 Psi(2, 2/3)
_______________________________________________________________________
3 1/2
12 Pi 3 + 14 Zeta(3) + 5 Psi(2, 1/4) + 5 Psi(2, 3/4) - 3 Psi(2, 5/6)
_______________________________________________________________________
- 8 Psi(2, 1/4) + Psi(2, 1/8) + Psi(2, 5/8)
_______________________________________________________________________
11
6048 Zeta(3) + 2 Psi(2, 1/12) + 16 Psi(2, 5/6) - 2 Psi(2, ----)
12
+ 7 Psi(2, 3/8) + 7 Psi(2, 7/8)
_______________________________________________________________________
11
- 8 Psi(2, 5/6) + Psi(2, 5/12) + Psi(2, ----)
12
_______________________________________________________________________
- 8 Psi(2, 1/6) + Psi(2, 1/12) + Psi(2, 7/12)
_______________________________________________________________________
3
- 104 Pi + 63 Psi(2, 1/3) - 52 Psi(2, 1/4) + 7 Psi(2, 5/6)
_______________________________________________________________________
3
- 26 Pi - 2 Psi(2, 1/6) + 13 Psi(2, 3/4) - 2 Psi(2, 5/6)
_______________________________________________________________________
- 8 Psi(2, 3/4) + Psi(2, 3/8) + Psi(2, 7/8)
_______________________________________________________________________
3
- 56 Pi - 1456 Zeta(3) - Psi(2, 1/12) - Psi(2, 5/12)
_______________________________________________________________________
3
108 Pi + Psi(2, 1/12) - 26 Psi(2, 3/4) + Psi(2, 5/12)
_______________________________________________________________________
3 1/2
8 Pi 2 + Psi(2, 3/4) - Psi(2, 5/12)
_______________________________________________________________________
3 1/2
30 Pi 3 + 8 Psi(2, 1/5) + 15 Psi(2, 1/6) - 2 Psi(2, 3/4) - 18 Psi(2, 5/6)
_______________________________________________________________________