Some Challenges for Wadim Zudlin By Shalosh B. Ekhad As usual let 3F2(a1,a2,a3;b1,b2;1) be the sum of (a1)_n*(a2)_n*(a3)_n/(n!*(b\ 1)_n*(b2)_n),n=0..infinity The following bunch of evaluations feature log(2) They are probably equivalent to each other (and some of them we can ourselv\ es 3F2(1,1,1/2;2,3/2;1) = 2 ln(2) 3F2(1,1,1/2;2,2;1) = 4 - 4 ln(2) 3F2(1,1,1/2;5/2,2;1) = -3 + 6 ln(2) 3F2(1,1,1/2;3/2,2;1) = 2 ln(2) 3F2(1,3/2,1;5/2,2;1) = 6 - 6 ln(2) 3F2(1,3/2,1;3,2;1) = -4 + 8 ln(2) 3F2(1,3/2,1;3,5/2;1) = 18 - 24 ln(2) 3F2(1,3/2,1;2,2;1) = 4 ln(2) 3F2(1,3/2,1;2,5/2;1) = 6 - 6 ln(2) The following bunch of evaluations feature Pi*sqrt(3) They are probably equivalent to each other 1/2 4 Pi 3 3F2(1,1,2/3;2,7/3;1) = -6 + --------- 3 1/2 Pi 3 3F2(1,1,2/3;2,4/3;1) = ------- 3 1/2 Pi 3 3F2(1,1,1/3;2,5/3;1) = 3 - ------- 3 1/2 Pi 3 3F2(1,1,1/3;2,2/3;1) = 3/2 + ------- 6 1/2 5 Pi 3 3F2(1,1,1/3;8/3,2;1) = 45/8 - --------- 6 1/2 4 Pi 3 3F2(1,1,2/3;7/3,2;1) = -6 + --------- 3 1/2 Pi 3 3F2(1,1,1/3;5/3,2;1) = 3 - ------- 3 1/2 Pi 3 3F2(1,1,2/3;4/3,2;1) = ------- 3 1/2 20 Pi 3 3F2(1,5/3,4/3;8/3,7/3;1) = -10 + ---------- 9 1/2 5 Pi 3 3F2(1,5/3,1/3;8/3,4/3;1) = 5/8 + --------- 36 1/2 7 Pi 3 3F2(1,5/3,1;10/3,2;1) = 63/8 - --------- 6 1/2 70 Pi 3 3F2(1,5/3,4/3;10/3,8/3;1) = - 245/6 + ---------- 9 1/2 8 Pi 3 3F2(1,5/3,1;3,7/3;1) = 16 - --------- 3 1/2 Pi 3 3F2(1,5/3,1;3,4/3;1) = 1 + ------- 3 1/2 2 Pi 3 3F2(1,5/3,1;7/3,2;1) = 6 - --------- 3 1/2 20 Pi 3 3F2(1,5/3,4/3;7/3,8/3;1) = -10 + ---------- 9 1/2 2 Pi 3 3F2(1,5/3,1;2,7/3;1) = 6 - --------- 3 1/2 Pi 3 3F2(1,5/3,1;2,4/3;1) = - 3/2 - ------- 6 1/2 4 Pi 3 3F2(1,4/3,2/3;7/3,5/3;1) = 4 - --------- 9 1/2 20 Pi 3 3F2(1,4/3,1;3,8/3;1) = -35 + ---------- 3 1/2 2 Pi 3 3F2(1,4/3,1;3,5/3;1) = -2 + --------- 3 1/2 5 Pi 3 3F2(1,4/3,1;8/3,2;1) = - 15/2 + --------- 3 1/2 20 Pi 3 3F2(1,4/3,2/3;8/3,7/3;1) = 40/3 - ---------- 9 1/2 5 Pi 3 3F2(1,4/3,1;2,8/3;1) = - 15/2 + --------- 3 1/2 2 Pi 3 3F2(1,4/3,1;2,5/3;1) = --------- 3 1/2 2 Pi 3 3F2(1,4/3,1;5/3,2;1) = --------- 3 1/2 4 Pi 3 3F2(1,4/3,2/3;5/3,7/3;1) = 4 - --------- 9 1/2 2 Pi 3 3F2(1,2/3,1/3;5/3,4/3;1) = --------- 9 1/2 4 Pi 3 3F2(1,2/3,1/3;7/3,5/3;1) = - 4/3 + --------- 9 1/2 2 Pi 3 3F2(1,2/3,1/3;4/3,5/3;1) = --------- 9 The following bunch of evaluations feature sqrt(2) They are probably equivalent to each other 1/2 48 + 64 2 3F2(1,7/4,5/4;7/2,3;1) = - ------------- 1/2 -51 - 36 2 1/2 4 + 12 2 3F2(1,7/4,5/4;7/2,5/2;1) = - ----------- 1/2 -7 - 5 2 1/2 8 + 16 2 3F2(1,7/4,5/4;7/2,2;1) = - ----------- 1/2 -9 - 6 2 1/2 12 + 4 2 3F2(1,7/4,5/4;7/2,3/2;1) = - ----------- 1/2 -3 - 3 2 1/2 8 - 56 2 3F2(1,7/4,1/4;7/2,2;1) = - ------------ 1/2 27 + 27 2 1/2 76 32 2 3F2(1,7/4,1/4;7/2,3/2;1) = -- - ------- 27 27 1/2 8 2 3F2(1,7/4,1/4;7/2,1;1) = ------ 9 20 3F2(1,7/4,1/4;7/2,1/2;1) = - ------------ 1/2 27 - 27 2 1/2 -24 - 24 2 3F2(1,7/4,7/4;13/4,3;1) = - ------------- 1/2 17 + 12 2 1/2 6 + 2 3F2(1,7/4,7/4;13/4,2;1) = - --------- 1/2 -1 - 2 1/2 -3 - 6 2 3F2(1,7/4,3/4;13/4,2;1) = - ----------- 1/2 4 + 3 2 1/2 15 2 3F2(1,7/4,3/4;13/4,1;1) = ------- 8 1/2 40 + 80 2 3F2(1,7/4,7/4;3,9/4;1) = - ------------- 1/2 -27 - 18 2 1/2 16 - 32 2 3F2(1,7/4,5/4;3,5/2;1) = - ------------ 1/2 9 + 6 2 1/2 16 + 48 2 3F2(1,7/4,5/4;3,3/2;1) = - ------------ 1/2 -9 - 9 2 1/2 8 2 3F2(1,7/4,3/4;3,9/4;1) = ---------- 1/2 4 + 3 2 1/2 -72 - 8 2 3F2(1,7/4,3/4;3,5/4;1) = - ------------ 1/2 15 + 15 2 1/2 1/2 (-128 + 16 2 ) 2 3F2(1,7/4,1/4;3,3/2;1) = - --------------------- 126 1/2 112 + 192 2 3F2(1,7/4,1/4;3,1/2;1) = - -------------- 1/2 -63 - 63 2 20 3F2(1,7/4,7/4;9/4,2;1) = - ----------- 1/2 -9 + 9 2 1/2 10 2 3F2(1,7/4,3/4;9/4,2;1) = ---------- 1/2 3 + 3 2 1/2 5 2 3F2(1,7/4,3/4;9/4,1;1) = - ------ 2 1/2 16 - 32 2 3F2(1,7/4,5/4;5/2,3;1) = - ------------ 1/2 9 + 6 2 12 3F2(1,7/4,5/4;5/2,5/2;1) = ---------- 1/2 3 + 2 2 1/2 8 + 8 2 3F2(1,7/4,5/4;5/2,2;1) = - ----------- 1/2 -3 - 2 2 1/2 -8 - 24 2 3F2(1,7/4,1/4;5/2,2;1) = - ------------ 1/2 15 + 15 2 1/2 4 + 8 2 3F2(1,7/4,1/4;5/2,3/2;1) = - ----------- 1/2 -5 - 5 2 1/2 12 + 6 2 3F2(1,7/4,1/4;5/2,1;1) = - ----------- 1/2 -5 - 5 2 1/2 8 + 8 2 3F2(1,7/4,5/4;2,5/2;1) = - ----------- 1/2 -3 - 2 2 1/2 4 + 6 2 3F2(1,7/4,5/4;2,3/2;1) = - ---------- 1/2 3 + 3 2 1/2 10 2 3F2(1,7/4,3/4;2,9/4;1) = ---------- 1/2 3 + 3 2 1/2 12 + 4 2 3F2(1,7/4,3/4;2,5/4;1) = - ----------- 1/2 3 + 3 2 1/2 4 2 3F2(1,7/4,1/4;2,3/2;1) = 8/9 + ------ 9 1/2 -2 + 3 2 3F2(1,7/4,1/4;2,1/2;1) = - ----------- 1/2 9 + 9 2 21 3F2(1,3/2,3/2;13/4,11/4;1) = ---------- 1/2 7 + 5 2 1/2 3 + 9 2 3F2(1,3/2,3/2;13/4,7/4;1) = - ----------- 1/2 -4 - 2 2 1/2 9 - 21 2 3F2(1,3/2,1/2;13/4,7/4;1) = - ----------- 1/2 7 + 7 2 1/2 1/2 (15 + 3 2 ) 2 3F2(1,3/2,1/2;13/4,3/4;1) = ------------------ 14 1/2 35 2 3F2(1,3/2,3/2;11/4,9/4;1) = ----------- 1/2 12 + 8 2 1/2 7 2 3F2(1,3/2,1/2;11/4,9/4;1) = ---------- 1/2 4 + 3 2 1/2 -7 - 14 2 3F2(1,3/2,1/2;11/4,5/4;1) = - ------------ 1/2 10 + 5 2 1/2 5 2 3F2(1,3/2,1/2;9/4,7/4;1) = ---------- 1/2 2 + 2 2 1/2 5 2 3F2(1,3/2,1/2;7/4,9/4;1) = ---------- 1/2 2 + 2 2 1/2 56 + 56 2 3F2(1,5/4,5/4;3,11/4;1) = - ------------- 1/2 -51 - 36 2 1/2 8 + 16 2 3F2(1,5/4,5/4;3,7/4;1) = - ----------- 1/2 -9 - 6 2 1/2 16 + 48 2 3F2(1,5/4,3/4;3,5/2;1) = - ------------- 1/2 -35 - 25 2 1/2 16 - 48 2 3F2(1,5/4,3/4;3,3/2;1) = - ------------ 1/2 15 + 15 2 1/2 24 - 56 2 3F2(1,5/4,1/4;3,7/4;1) = - ------------ 1/2 21 + 21 2 1/2 64 2 3F2(1,5/4,1/4;3,3/4;1) = - 8/63 + ------- 63 1/2 7 2 3F2(1,5/4,5/4;11/4,2;1) = ---------- 1/2 3 + 2 2 1/2 7 + 14 2 3F2(1,5/4,1/4;11/4,2;1) = - ------------ 1/2 -12 - 9 2 1/2 7 2 3F2(1,5/4,1/4;11/4,1;1) = ------ 8 1/2 4 - 8 2 3F2(1,5/4,3/4;5/2,5/2;1) = - ---------- 1/2 3 + 2 2 1/2 8 2 3F2(1,5/4,3/4;5/2,2;1) = ---------- 1/2 4 + 3 2 1/2 -4 - 4 2 3F2(1,5/4,3/4;5/2,3/2;1) = - ----------- 1/2 3 + 2 2 1/2 3F2(1,5/4,3/4;5/2,1;1) = 2 2 1/2 2 2 3F2(1,5/4,1/4;7/4,2;1) = -------- 1/2 1 + 2 1/2 3 2 3F2(1,5/4,1/4;7/4,1;1) = ------ 2 12 3F2(1,5/4,5/4;2,7/4;1) = -------- 1/2 1 + 2 1/2 8 2 3F2(1,5/4,3/4;2,5/2;1) = ---------- 1/2 4 + 3 2 1/2 4 2 3F2(1,5/4,3/4;2,3/2;1) = -------- 1/2 1 + 2 1/2 2 2 3F2(1,5/4,1/4;2,7/4;1) = -------- 1/2 1 + 2 1/2 12 + 4 2 3F2(1,5/4,1/4;2,3/4;1) = - ----------- 1/2 -3 - 3 2 1/2 -4 - 4 2 3F2(1,5/4,3/4;3/2,5/2;1) = - ----------- 1/2 3 + 2 2 1/2 4 2 3F2(1,5/4,3/4;3/2,2;1) = -------- 1/2 1 + 2 1/2 2 3F2(1,5/4,3/4;3/2,1;1) = - ---- 2 1/2 -15 + 5 2 3F2(1,1/2,1/2;9/4,7/4;1) = - ------------ 1/2 3 + 3 2 1/2 5 2 3F2(1,1/2,1/2;9/4,3/4;1) = 5/9 + ------ 9 1/2 3 2 3F2(1,1/2,1/2;7/4,5/4;1) = -------- 1/2 2 + 2 1/2 -8 - 16 2 3F2(1,3/4,1/4;5/2,2;1) = - ------------ 1/2 15 + 10 2 1/2 4 - 12 2 3F2(1,3/4,1/4;5/2,3/2;1) = - ----------- 1/2 5 + 5 2 1/2 4 2 3F2(1,3/4,1/4;5/2,1;1) = ------ 5 1/2 2 2 3F2(1,3/4,1/4;5/2,1/2;1) = 4/5 + ------ 5 1/2 5 2 3F2(1,3/4,3/4;9/4,2;1) = ---------- 1/2 3 + 2 2 1/2 5 2 3F2(1,3/4,3/4;9/4,1;1) = ------ 4 1/2 -4 - 4 2 3F2(1,3/4,3/4;2,5/4;1) = - ----------- 1/2 3 + 2 2 8 3F2(1,3/4,1/4;2,3/2;1) = ---------- 1/2 3 + 3 2 1/2 -4 - 6 2 3F2(1,3/4,1/4;2,1/2;1) = - ----------- 1/2 3 + 3 2 1/2 3F2(1,3/4,3/4;5/4,1;1) = -2 8 3F2(1,3/4,1/4;3/2,2;1) = ---------- 1/2 3 + 3 2 1/2 2 2 3F2(1,3/4,1/4;3/2,3/2;1) = -------- 1/2 1 + 2 1/2 3F2(1,3/4,1/4;3/2,1;1) = 2 1/2 3F2(1,3/4,1/4;1,3/2;1) = 2 1/2 2 3F2(1,3/4,1/4;1,1/2;1) = ---- 4 1/2 5 2 3F2(1,1/4,1/4;2,7/4;1) = - 4/3 + ------ 3 1/2 4 2 3F2(1,1/4,1/4;2,3/4;1) = 4/9 + ------ 9 1/2 3 2 3F2(1,1/4,1/4;7/4,1;1) = ------ 4 1/2 3F2(1,1/4,1/4;1,3/4;1) = 2 The following bunch of evaluations feature sqrt(5) They are probably equivalent to each other 1/2 130 - 195 5 3F2(1,9/5,7/5;18/5,3;1) = - -------------- 1/2 108 + 48 5 65 3F2(1,9/5,7/5;18/5,2;1) = ----------- 1/2 16 + 8 5 1/2 13 - 65 5 3F2(1,9/5,6/5;18/5,12/5;1) = - ------------ 1/2 44 + 20 5 1/2 39 5 3F2(1,9/5,6/5;18/5,7/5;1) = - 26/7 + ------- 14 1/2 -65 - 260 5 3F2(1,9/5,2/5;18/5,2;1) = - -------------- 1/2 264 + 132 5 1/2 13 13 5 3F2(1,9/5,2/5;18/5,1;1) = - -- + ------- 11 11 1/2 117 - 143 5 3F2(1,9/5,1/5;18/5,7/5;1) = - -------------- 1/2 56 + 56 5 1/2 13 5 3F2(1,9/5,1/5;18/5,2/5;1) = ------- 16 1/2 22 + 2 5 3F2(1,9/5,6/5;17/5,13/5;1) = - ----------- 1/2 -9 - 4 5 1/2 -1 - 5 5 3F2(1,9/5,6/5;17/5,8/5;1) = - ----------- 1/2 3 + 5 1/2 12 - 23 5 3F2(1,9/5,1/5;17/5,8/5;1) = - ------------ 1/2 11 + 11 5 1/2 7 5 3F2(1,9/5,1/5;17/5,3/5;1) = 1/11 + ------ 11 1/2 55 - 55 5 3F2(1,9/5,8/5;16/5,3;1) = - ------------ 1/2 21 + 9 5 55 3F2(1,9/5,8/5;16/5,2;1) = ---------- 1/2 6 + 6 5 1/2 55 5 3F2(1,9/5,3/5;16/5,2;1) = ------------ 1/2 40 + 24 5 11 3F2(1,9/5,3/5;16/5,1;1) = - ---------- 1/2 4 - 4 5 1/2 55 - 55 5 3F2(1,9/5,8/5;3,16/5;1) = - ------------ 1/2 21 + 9 5 1/2 5 - 15 5 3F2(1,9/5,8/5;3,11/5;1) = - ----------- 1/2 6 + 2 5 1/2 20 - 20 5 3F2(1,9/5,7/5;3,13/5;1) = - ------------ 1/2 7 + 3 5 1/2 40 + 5 5 3F2(1,9/5,7/5;3,8/5;1) = - ----------- 1/2 -6 - 2 5 1/2 -5 - 15 5 3F2(1,9/5,3/5;3,11/5;1) = - ------------ 1/2 14 + 7 5 1/2 -80 - 5 5 3F2(1,9/5,3/5;3,6/5;1) = - ------------ 1/2 14 + 14 5 1/2 5 + 10 5 3F2(1,9/5,2/5;3,8/5;1) = - ------------ 1/2 -12 - 4 5 1/2 5 - 45 5 3F2(1,9/5,2/5;3,3/5;1) = - ----------- 1/2 8 + 8 5 1/2 20 - 20 5 3F2(1,9/5,7/5;13/5,3;1) = - ------------ 1/2 7 + 3 5 1/2 10 5 3F2(1,9/5,7/5;13/5,2;1) = -------- 1/2 3 + 5 1/2 7 - 7 5 3F2(1,9/5,6/5;13/5,12/5;1) = - ---------- 1/2 2 + 5 1/2 5 + 5 5 3F2(1,9/5,2/5;13/5,2;1) = - ----------- 1/2 -6 - 3 5 1/2 3F2(1,9/5,2/5;13/5,1;1) = -2 + 2 5 1/2 8 - 16 5 3F2(1,9/5,1/5;13/5,7/5;1) = - ----------- 1/2 7 + 7 5 1/2 7 - 7 5 3F2(1,9/5,6/5;12/5,13/5;1) = - ---------- 1/2 2 + 5 1/2 7 5 3F2(1,9/5,1/5;12/5,8/5;1) = ---------- 1/2 4 + 4 5 1/2 5 - 15 5 3F2(1,9/5,8/5;11/5,3;1) = - ----------- 1/2 6 + 2 5 5 3F2(1,9/5,8/5;11/5,2;1) = - -------- 1/2 3 - 5 1/2 5 5 3F2(1,9/5,3/5;11/5,2;1) = ---------- 1/2 2 + 2 5 1/2 3F2(1,9/5,3/5;11/5,1;1) = -5 - 1 55 3F2(1,9/5,8/5;2,16/5;1) = ---------- 1/2 6 + 6 5 5 3F2(1,9/5,8/5;2,11/5;1) = - -------- 1/2 3 - 5 1/2 10 5 3F2(1,9/5,7/5;2,13/5;1) = -------- 1/2 3 + 5 1/2 15 - 10 5 3F2(1,9/5,7/5;2,8/5;1) = - ------------ 1/2 4 - 4 5 1/2 5 5 3F2(1,9/5,3/5;2,11/5;1) = ---------- 1/2 2 + 2 5 1/2 20 + 5 5 3F2(1,9/5,3/5;2,6/5;1) = - ----------- 1/2 4 + 4 5 5 3F2(1,9/5,2/5;2,8/5;1) = - ---------- 1/2 2 - 2 5 1/2 10 - 15 5 3F2(1,8/5,6/5;17/5,3;1) = - ------------ 1/2 9 + 4 5 1/2 10 5 3F2(1,8/5,6/5;17/5,2;1) = ---------- 1/2 7 + 3 5 1/2 -5 - 20 5 3F2(1,8/5,1/5;17/5,2;1) = - ------------ 1/2 22 + 11 5 1/2 21 21 5 3F2(1,8/5,1/5;17/5,1;1) = - -- + ------- 22 22 33 3F2(1,8/5,7/5;16/5,14/5;1) = ----------- 1/2 11 + 5 5 1/2 11 5 3F2(1,8/5,7/5;16/5,9/5;1) = - 11/6 + ------- 6 1/2 55 5 3F2(1,8/5,4/5;16/5,2;1) = ------------ 1/2 42 + 21 5 1/2 11 11 5 3F2(1,8/5,4/5;16/5,1;1) = -- + ------- 14 14 1/2 44 - 66 5 3F2(1,8/5,2/5;16/5,9/5;1) = - ------------ 1/2 27 + 27 5 1/2 22 11 5 3F2(1,8/5,2/5;16/5,4/5;1) = -- + ------- 27 27 35 3F2(1,8/5,6/5;3,12/5;1) = ----------- 1/2 11 + 5 5 1/2 15 - 35 5 3F2(1,8/5,6/5;3,7/5;1) = - ------------ 1/2 6 + 6 5 1/2 5 - 10 5 3F2(1,8/5,4/5;3,11/5;1) = - ----------- 1/2 6 + 3 5 1/2 25 5 3F2(1,8/5,4/5;3,6/5;1) = - 5/6 + ------- 18 1/2 25 5 3F2(1,8/5,1/5;3,7/5;1) = - 5/12 + ------- 36 1/2 -70 - 15 5 3F2(1,8/5,1/5;3,2/5;1) = - ------------- 1/2 27 + 9 5 33 3F2(1,8/5,7/5;14/5,16/5;1) = ----------- 1/2 11 + 5 5 9 3F2(1,8/5,7/5;14/5,11/5;1) = -------- 1/2 2 + 5 1/2 -9 - 27 5 3F2(1,8/5,2/5;14/5,11/5;1) = - ------------ 1/2 28 + 14 5 1/2 6 5 3F2(1,8/5,2/5;14/5,6/5;1) = - 3/7 + ------ 7 35 3F2(1,8/5,6/5;12/5,3;1) = ----------- 1/2 11 + 5 5 35 3F2(1,8/5,6/5;12/5,2;1) = ---------- 1/2 6 + 3 5 1/2 35 - 35 5 3F2(1,8/5,1/5;12/5,2;1) = - ------------ 1/2 12 + 12 5 1/2 7 5 3F2(1,8/5,1/5;12/5,1;1) = - 7/6 + ------ 6 9 3F2(1,8/5,7/5;11/5,14/5;1) = -------- 1/2 2 + 5 1/2 -5 - 5 5 3F2(1,8/5,4/5;11/5,2;1) = - ----------- 1/2 4 + 2 5 1/2 3 5 3F2(1,8/5,4/5;11/5,1;1) = - 3/2 - ------ 2 1/2 2 5 3F2(1,8/5,2/5;11/5,9/5;1) = -------- 1/2 5 + 1 35 3F2(1,8/5,6/5;2,12/5;1) = ---------- 1/2 6 + 3 5 1/2 10 5 3F2(1,8/5,6/5;2,7/5;1) = - ---------- 1/2 3 + 3 5 1/2 -5 - 5 5 3F2(1,8/5,4/5;2,11/5;1) = - ----------- 1/2 4 + 2 5 1/2 5 5 3F2(1,8/5,4/5;2,6/5;1) = - ------ 3 5 3F2(1,8/5,1/5;2,7/5;1) = - ---------- 1/2 3 - 3 5 1/2 11 5 3F2(1,8/5,7/5;9/5,16/5;1) = - 11/6 + ------- 6 1/2 2 5 3F2(1,8/5,2/5;9/5,11/5;1) = -------- 1/2 5 + 1 1/2 44 + 11 5 3F2(1,7/5,3/5;16/5,9/5;1) = - ------------- 1/2 -28 - 12 5 1/2 55 + 22 5 3F2(1,7/5,3/5;16/5,4/5;1) = - ------------- 1/2 -16 - 16 5 1/2 15 - 15 5 3F2(1,7/5,6/5;3,14/5;1) = - ------------ 1/2 7 + 3 5 1/2 5 - 15 5 3F2(1,7/5,6/5;3,9/5;1) = - ----------- 1/2 9 + 3 5 1/2 55 + 5 5 3F2(1,7/5,4/5;3,13/5;1) = - ------------- 1/2 -27 - 12 5 1/2 5 + 15 5 3F2(1,7/5,4/5;3,8/5;1) = - ------------ 1/2 -12 - 6 5 1/2 45 + 35 5 3F2(1,7/5,1/5;3,9/5;1) = - ------------- 1/2 -54 - 27 5 1/2 5 - 10 5 3F2(1,7/5,1/5;3,4/5;1) = - ------------ 1/2 54 - 18 5 1/2 15 - 15 5 3F2(1,7/5,6/5;14/5,3;1) = - ------------ 1/2 7 + 3 5 15 3F2(1,7/5,6/5;14/5,2;1) = ---------- 1/2 4 + 2 5 1/2 3 - 6 5 3F2(1,7/5,3/5;14/5,11/5;1) = - ---------- 1/2 4 + 2 5 1/2 3 5 3F2(1,7/5,3/5;14/5,6/5;1) = ------ 4 45 3F2(1,7/5,1/5;14/5,2;1) = ----------- 1/2 24 + 8 5 3 3F2(1,7/5,1/5;14/5,1;1) = - ---------- 1/2 2 - 2 5 1/2 5 - 5 5 3F2(1,7/5,4/5;13/5,2;1) = - ---------- 1/2 2 + 5 1/2 3F2(1,7/5,4/5;13/5,1;1) = -3 + 3 5 1/2 -2 - 2 5 3F2(1,7/5,3/5;11/5,9/5;1) = - ----------- 1/2 2 + 5 15 3F2(1,7/5,6/5;2,14/5;1) = ---------- 1/2 4 + 2 5 1/2 3F2(1,7/5,6/5;2,9/5;1) = -5 + 5 5 1/2 5 - 5 5 3F2(1,7/5,4/5;2,13/5;1) = - ---------- 1/2 2 + 5 1/2 15 5 3F2(1,7/5,4/5;2,8/5;1) = ---------- 1/2 5 + 3 5 1/2 5 5 3F2(1,7/5,1/5;2,9/5;1) = ---------- 1/2 3 + 3 5 1/2 20 + 5 5 3F2(1,7/5,1/5;2,4/5;1) = - ----------- 1/2 -4 - 4 5 1/2 5 - 15 5 3F2(1,7/5,6/5;9/5,3;1) = - ----------- 1/2 9 + 3 5 1/2 3F2(1,7/5,6/5;9/5,2;1) = -5 + 5 5 1/2 -2 - 2 5 3F2(1,7/5,3/5;9/5,11/5;1) = - ----------- 1/2 2 + 5 1/2 5 5 3F2(1,7/5,1/5;9/5,2;1) = ---------- 1/2 3 + 3 5 1/2 2 5 3F2(1,7/5,1/5;9/5,1;1) = 2/3 + ------ 3 1/2 15 5 3F2(1,7/5,4/5;8/5,2;1) = ---------- 1/2 5 + 3 5 2 3F2(1,7/5,4/5;8/5,1;1) = - -------- 1/2 5 + 1 1/2 5 - 25 5 3F2(1,6/5,3/5;3,12/5;1) = - ------------ 1/2 22 + 10 5 1/2 -60 + 5 5 3F2(1,6/5,3/5;3,7/5;1) = - ------------ 1/2 21 + 7 5 1/2 -5 - 15 5 3F2(1,6/5,2/5;3,9/5;1) = - ------------ 1/2 16 + 8 5 1/2 -35 - 10 5 3F2(1,6/5,2/5;3,4/5;1) = - ------------- 1/2 12 + 12 5 1/2 15 5 3F2(1,6/5,2/5;14/5,2;1) = ----------- 1/2 14 + 7 5 1/2 3 5 3F2(1,6/5,2/5;14/5,1;1) = 3/7 + ------ 7 1/2 7 + 7 5 3F2(1,6/5,4/5;13/5,12/5;1) = - ----------- 1/2 -9 - 4 5 1/2 -5 - 5 3F2(1,6/5,4/5;13/5,7/5;1) = - --------- 1/2 2 + 5 1/2 7 + 7 5 3F2(1,6/5,4/5;12/5,13/5;1) = - ----------- 1/2 -9 - 4 5 7 3F2(1,6/5,4/5;12/5,8/5;1) = -------- 1/2 2 + 5 35 3F2(1,6/5,3/5;12/5,2;1) = ----------- 1/2 14 + 6 5 1/2 7 5 3F2(1,6/5,3/5;12/5,1;1) = -------- 1/2 5 + 5 35 3F2(1,6/5,3/5;2,12/5;1) = ----------- 1/2 14 + 6 5 1/2 -5 - 5 5 3F2(1,6/5,3/5;2,7/5;1) = - ----------- 1/2 4 + 2 5 1/2 5 + 5 5 3F2(1,6/5,2/5;2,9/5;1) = - ----------- 1/2 -6 - 3 5 1/2 5 5 3F2(1,6/5,2/5;2,4/5;1) = ------ 3 1/2 5 + 5 5 3F2(1,6/5,2/5;9/5,2;1) = - ----------- 1/2 -6 - 3 5 1/2 3F2(1,6/5,2/5;9/5,1;1) = 5 + 1 7 3F2(1,6/5,4/5;8/5,12/5;1) = -------- 1/2 2 + 5 1/2 -5 - 5 3F2(1,6/5,4/5;7/5,13/5;1) = - --------- 1/2 2 + 5 1/2 -5 - 5 5 3F2(1,6/5,3/5;7/5,2;1) = - ----------- 1/2 4 + 2 5 2 3F2(1,6/5,3/5;7/5,1;1) = - -------- 1/2 5 + 1 1/2 20 5 3F2(1,4/5,2/5;13/5,2;1) = ----------- 1/2 21 + 9 5 1/2 3F2(1,4/5,2/5;13/5,1;1) = 5 - 1 1/2 7 + 11 5 3F2(1,4/5,1/5;13/5,7/5;1) = - ------------ 1/2 -14 - 7 5 1/2 3 5 3F2(1,4/5,1/5;13/5,2/5;1) = 3/7 + ------ 7 1/2 21 - 14 5 3F2(1,4/5,1/5;12/5,8/5;1) = - ------------ 1/2 3 + 3 5 1/2 7 5 3F2(1,4/5,1/5;12/5,3/5;1) = 7/18 + ------ 18 1/2 5 - 5 5 3F2(1,4/5,3/5;11/5,2;1) = - ---------- 1/2 3 + 5 2 3F2(1,4/5,3/5;11/5,1;1) = - --------- 1/2 -5 + 1 1/2 5 - 5 5 3F2(1,4/5,3/5;2,11/5;1) = - ---------- 1/2 3 + 5 5 3F2(1,4/5,3/5;2,6/5;1) = -------- 1/2 5 + 1 1/2 5 - 5 5 3F2(1,4/5,2/5;2,8/5;1) = - ---------- 1/2 3 + 5 1/2 10 5 3F2(1,4/5,2/5;2,3/5;1) = ---------- 1/2 3 + 3 5 1/2 5 - 5 5 3F2(1,4/5,2/5;8/5,2;1) = - ---------- 1/2 3 + 5 1/2 3 + 3 5 3F2(1,4/5,2/5;8/5,1;1) = - ---------- 1/2 -3 - 5 6 3F2(1,4/5,1/5;8/5,7/5;1) = -------- 1/2 3 + 5 6 3F2(1,4/5,1/5;7/5,8/5;1) = -------- 1/2 3 + 5 5 3F2(1,4/5,3/5;6/5,2;1) = -------- 1/2 5 + 1 2 3F2(1,4/5,3/5;6/5,1;1) = - -------- 1/2 5 - 1 2 3F2(1,4/5,3/5;1,11/5;1) = - --------- 1/2 -5 + 1 2 3F2(1,4/5,3/5;1,6/5;1) = - -------- 1/2 5 - 1 1/2 3 + 3 5 3F2(1,4/5,2/5;1,8/5;1) = - ---------- 1/2 -3 - 5 2 3F2(1,4/5,2/5;1,3/5;1) = ---------- 1/2 3 + 3 5 1/2 35 5 3F2(1,3/5,1/5;12/5,2;1) = ------------ 1/2 40 + 16 5 7 3F2(1,3/5,1/5;12/5,1;1) = ---------- 1/2 2 + 2 5 1/2 1 - 3 5 3F2(1,3/5,2/5;11/5,9/5;1) = - ---------- 1/2 3 + 5 1 3F2(1,3/5,2/5;11/5,4/5;1) = - -------- 1/2 5 - 3 1/2 5 5 3F2(1,3/5,1/5;2,7/5;1) = ---------- 1/2 6 + 2 5 1/2 -15 + 10 5 3F2(1,3/5,1/5;2,2/5;1) = - ------------- 1/2 4 - 4 5 1/2 1 - 3 5 3F2(1,3/5,2/5;9/5,11/5;1) = - ---------- 1/2 3 + 5 1/2 3F2(1,3/5,2/5;9/5,6/5;1) = 5 - 1 1/2 5 5 3F2(1,3/5,1/5;7/5,2;1) = ---------- 1/2 6 + 2 5 1/2 3F2(1,3/5,1/5;7/5,1;1) = 5 - 1 1/2 3F2(1,3/5,2/5;6/5,9/5;1) = 5 - 1 1/2 3F2(1,3/5,1/5;1,7/5;1) = 5 - 1 1 3F2(1,3/5,1/5;1,2/5;1) = -------- 1/2 5 + 1 1 3F2(1,3/5,2/5;4/5,11/5;1) = - -------- 1/2 5 - 3 1/2 5 + 5 5 3F2(1,2/5,1/5;2,9/5;1) = - ----------- 1/2 -9 - 3 5 1/2 10 + 5 5 3F2(1,2/5,1/5;2,4/5;1) = - ----------- 1/2 -6 - 6 5 1/2 5 + 5 5 3F2(1,2/5,1/5;9/5,2;1) = - ----------- 1/2 -9 - 3 5 4 3F2(1,2/5,1/5;9/5,1;1) = - ---------- 1/2 3 - 3 5 4 3F2(1,2/5,1/5;1,9/5;1) = - ---------- 1/2 3 - 3 5 2 3F2(1,2/5,1/5;1,4/5;1) = - --------- 1/2 -5 + 1 1/2 10 + 5 5 3F2(1,2/5,1/5;4/5,2;1) = - ----------- 1/2 -6 - 6 5 2 3F2(1,2/5,1/5;4/5,1;1) = - --------- 1/2 -5 + 1 The following bunch of evaluations feature sqrt(3) They are probably equivalent to each other 1/2 -1792 + 320 3 3F2(1,11/6,3/2;11/3,3;1) = - ---------------- 1/2 420 + 245 3 1/2 160 - 288 3 3F2(1,11/6,3/2;11/3,2;1) = - -------------- 1/2 105 + 35 3 1/2 -512 - 640 3 3F2(1,11/6,7/6;11/3,7/3;1) = - --------------- 1/2 540 + 315 3 1/2 1/2 (-256 + 32 3 ) 3 3F2(1,11/6,7/6;11/3,4/3;1) = - --------------------- 135 1/2 -544 - 1728 3 3F2(1,11/6,1/2;11/3,2;1) = - ---------------- 1/2 1365 + 910 3 1/2 256 3 3F2(1,11/6,1/2;11/3,1;1) = -------- 273 1/2 1/2 (512 - 544 3 ) 3 3F2(1,11/6,1/6;11/3,4/3;1) = - --------------------- 675 1/2 1/2 (128 + 64 3 ) 3 3F2(1,11/6,1/6;11/3,1/3;1) = -------------------- 225 1/2 16 + 52 3 3F2(1,11/6,7/6;10/3,8/3;1) = - ------------- 1/2 -36 - 21 3 1/2 1/2 (-128 + 40 3 ) 3 3F2(1,11/6,7/6;10/3,5/3;1) = - --------------------- 45 1/2 1/2 (256 - 360 3 ) 3 3F2(1,11/6,1/6;10/3,5/3;1) = - --------------------- 585 1/2 1/2 (224 + 140 3 ) 3 3F2(1,11/6,1/6;10/3,2/3;1) = --------------------- 585 1/2 13 3 3F2(1,11/6,3/2;19/6,3;1) = ---------- 1/2 7 + 4 3 1/2 -65 - 78 3 3F2(1,11/6,3/2;19/6,2;1) = - ------------- 1/2 40 + 20 3 1/2 65 - 117 3 3F2(1,11/6,1/2;19/6,2;1) = - ------------- 1/2 40 + 40 3 1/2 91 3 3F2(1,11/6,1/2;19/6,1;1) = ------- 80 1/2 13 3 3F2(1,11/6,3/2;3,19/6;1) = ---------- 1/2 7 + 4 3 1/2 32 + 8 3 3F2(1,11/6,3/2;3,8/3;1) = - ------------ 1/2 -12 - 7 3 1/2 28 3 3F2(1,11/6,3/2;3,13/6;1) = ----------- 1/2 10 + 5 3 1/2 80 + 64 3 3F2(1,11/6,3/2;3,5/3;1) = - ------------- 1/2 -15 - 10 3 14 3F2(1,11/6,1/2;3,13/6;1) = ---------- 1/2 6 + 3 3 1/2 -80 - 32 3 3F2(1,11/6,1/2;3,5/3;1) = - ------------- 1/2 45 + 30 3 1/2 28 32 3 3F2(1,11/6,1/2;3,7/6;1) = - -- + ------- 15 15 1/2 1/2 (56 - 104 3 ) 3 3F2(1,11/6,1/2;3,2/3;1) = - -------------------- 45 1/2 16 - 32 3 3F2(1,11/6,7/6;7/3,8/3;1) = - ------------ 1/2 9 + 6 3 1/2 1/2 (64 - 160 3 ) 3 3F2(1,11/6,1/6;7/3,5/3;1) = - -------------------- 315 1/2 32 + 8 3 3F2(1,11/6,3/2;8/3,3;1) = - ------------ 1/2 -12 - 7 3 1/2 1/2 (-16 + 4 3 ) 3 3F2(1,11/6,3/2;8/3,2;1) = - ------------------- 3 1/2 16 - 32 3 3F2(1,11/6,7/6;8/3,7/3;1) = - ------------ 1/2 9 + 6 3 1/2 12 - 52 3 3F2(1,11/6,1/2;8/3,2;1) = - ------------ 1/2 21 + 21 3 1/2 40 3 3F2(1,11/6,1/2;8/3,1;1) = ------- 21 1/2 1/2 (16 - 20 3 ) 3 3F2(1,11/6,1/6;8/3,4/3;1) = - ------------------- 27 1/2 28 3 3F2(1,11/6,3/2;13/6,3;1) = ----------- 1/2 10 + 5 3 1/2 -14 + 14 3 3F2(1,11/6,3/2;13/6,2;1) = - ------------- 1/2 10 - 5 3 1/2 7 3 3F2(1,11/6,1/2;13/6,2;1) = 14/5 - ------ 10 1/2 7 3 3F2(1,11/6,1/2;13/6,1;1) = - ------ 4 1/2 -65 - 78 3 3F2(1,11/6,3/2;2,19/6;1) = - ------------- 1/2 40 + 20 3 1/2 1/2 (-16 + 4 3 ) 3 3F2(1,11/6,3/2;2,8/3;1) = - ------------------- 3 1/2 -14 + 14 3 3F2(1,11/6,3/2;2,13/6;1) = - ------------- 1/2 10 - 5 3 1/2 1/2 (-2 + 8 3 ) 3 3F2(1,11/6,3/2;2,5/3;1) = - ------------------ 15 1/2 7 3 3F2(1,11/6,1/2;2,13/6;1) = 14/5 - ------ 10 1/2 1/2 (8 + 8 3 ) 3 3F2(1,11/6,1/2;2,5/3;1) = ----------------- 15 1/2 20 + 14 3 3F2(1,11/6,1/2;2,7/6;1) = - ------------ 1/2 10 + 5 3 1/2 1/2 (-7 + 8 3 ) 3 3F2(1,11/6,1/2;2,2/3;1) = - ------------------ 30 143 3F2(1,5/3,4/3;19/6,17/6;1) = ------------ 1/2 48 + 28 3 1/2 -65 - 78 3 3F2(1,5/3,4/3;19/6,11/6;1) = - ------------- 1/2 48 + 24 3 1/2 1/2 (91 - 78 3 ) 3 3F2(1,5/3,1/3;19/6,11/6;1) = - ------------------- 66 1/2 13 91 3 3F2(1,5/3,1/3;19/6,5/6;1) = -- + ------- 33 132 143 3F2(1,5/3,4/3;17/6,19/6;1) = ------------ 1/2 48 + 28 3 1/2 77 - 154 3 3F2(1,5/3,4/3;17/6,13/6;1) = - ------------- 1/2 48 + 24 3 1/2 77 3 3F2(1,5/3,1/3;17/6,13/6;1) = ------------ 1/2 54 + 36 3 1/2 55 3 3F2(1,5/3,1/3;17/6,7/6;1) = - 11/9 + ------- 36 1/2 77 - 154 3 3F2(1,5/3,4/3;13/6,17/6;1) = - ------------- 1/2 48 + 24 3 1/2 7 3 3F2(1,5/3,1/3;13/6,11/6;1) = 7/3 - ------ 12 1/2 -65 - 78 3 3F2(1,5/3,4/3;11/6,19/6;1) = - ------------- 1/2 48 + 24 3 1/2 7 3 3F2(1,5/3,1/3;11/6,13/6;1) = 7/3 - ------ 12 1/2 -224 + 40 3 3F2(1,3/2,7/6;10/3,3;1) = - -------------- 1/2 60 + 35 3 1/2 -92 + 24 3 3F2(1,3/2,7/6;10/3,2;1) = - ------------- 1/2 15 + 10 3 1/2 784 + 500 3 3F2(1,3/2,1/6;10/3,2;1) = - --------------- 1/2 -780 - 455 3 1/2 128 3 3F2(1,3/2,1/6;10/3,1;1) = -------- 195 1/2 -65 - 221 3 3F2(1,3/2,5/6;19/6,2;1) = - -------------- 1/2 160 + 96 3 1/2 91 3 3F2(1,3/2,5/6;19/6,1;1) = ------- 64 1/2 11 3 3F2(1,3/2,7/6;3,17/6;1) = ---------- 1/2 7 + 4 3 1/2 32 - 96 3 3F2(1,3/2,7/6;3,7/3;1) = - ------------ 1/2 45 + 25 3 1/2 4 3 3F2(1,3/2,7/6;3,11/6;1) = -------- 1/2 2 + 3 1/2 1/2 (16 - 24 3 ) 3 3F2(1,3/2,7/6;3,4/3;1) = - ------------------- 15 1/2 -32 - 104 3 3F2(1,3/2,5/6;3,8/3;1) = - -------------- 1/2 84 + 49 3 1/2 12 + 4 3 3F2(1,3/2,5/6;3,13/6;1) = - ----------- 1/2 -7 - 4 3 1/2 16 + 32 3 3F2(1,3/2,5/6;3,5/3;1) = - ------------- 1/2 -21 - 14 3 1/2 16 3 3F2(1,3/2,5/6;3,7/6;1) = - 12/7 + ------- 7 1/2 6 - 22 3 3F2(1,3/2,1/6;3,11/6;1) = - ------------ 1/2 11 + 11 3 1/2 1/2 (64 + 24 3 ) 3 3F2(1,3/2,1/6;3,4/3;1) = ------------------- 165 1/2 12 32 3 3F2(1,3/2,1/6;3,5/6;1) = -- + ------- 55 55 1/2 1/2 (56 - 144 3 ) 3 3F2(1,3/2,1/6;3,1/3;1) = - -------------------- 165 1/2 11 3 3F2(1,3/2,7/6;17/6,3;1) = ---------- 1/2 7 + 4 3 1/2 11 - 22 3 3F2(1,3/2,7/6;17/6,2;1) = - ------------ 1/2 8 + 4 3 1/2 55 - 99 3 3F2(1,3/2,1/6;17/6,2;1) = - ------------ 1/2 40 + 40 3 1/2 11 3 3F2(1,3/2,1/6;17/6,1;1) = ------- 16 1/2 4 - 8 3 3F2(1,3/2,5/6;8/3,2;1) = - ---------- 1/2 3 + 2 3 1/2 8 3 3F2(1,3/2,5/6;8/3,1;1) = ------ 3 1/2 11 - 22 3 3F2(1,3/2,7/6;2,17/6;1) = - ------------ 1/2 8 + 4 3 1/2 16 3 3F2(1,3/2,7/6;2,7/3;1) = ---------- 1/2 6 + 3 3 1/2 -10 - 10 3 3F2(1,3/2,7/6;2,11/6;1) = - ------------- 1/2 2 + 3 1/2 1/2 (-2 + 4 3 ) 3 3F2(1,3/2,7/6;2,4/3;1) = - ------------------ 3 1/2 4 - 8 3 3F2(1,3/2,5/6;2,8/3;1) = - ---------- 1/2 3 + 2 3 7 3F2(1,3/2,5/6;2,13/6;1) = -------- 1/2 2 + 3 1/2 -8 - 8 3 3F2(1,3/2,5/6;2,5/3;1) = - ----------- 1/2 3 + 2 3 1/2 8 + 6 3 3F2(1,3/2,5/6;2,7/6;1) = - ---------- 1/2 2 + 3 1/2 -1 - 3 3 3F2(1,3/2,1/6;2,11/6;1) = - ----------- 1/2 2 + 2 3 1/2 1/2 (4 + 4 3 ) 3 3F2(1,3/2,1/6;2,4/3;1) = ----------------- 15 1/2 -20 - 14 3 3F2(1,3/2,1/6;2,5/6;1) = - ------------- 1/2 10 + 5 3 1/2 1/2 (-7 + 8 3 ) 3 3F2(1,3/2,1/6;2,1/3;1) = - ------------------ 15 7 3F2(1,3/2,5/6;13/6,2;1) = -------- 1/2 2 + 3 1/2 7 3 3F2(1,3/2,5/6;13/6,1;1) = - ------ 2 1/2 32 - 96 3 3F2(1,3/2,7/6;7/3,3;1) = - ------------ 1/2 45 + 25 3 1/2 16 3 3F2(1,3/2,7/6;7/3,2;1) = ---------- 1/2 6 + 3 3 1/2 1/2 (128 - 112 3 ) 3 3F2(1,3/2,1/6;7/3,2;1) = - --------------------- 105 1/2 16 3 3F2(1,3/2,1/6;7/3,1;1) = ------- 21 1/2 4 3 3F2(1,3/2,7/6;11/6,3;1) = -------- 1/2 2 + 3 1/2 -10 - 10 3 3F2(1,3/2,7/6;11/6,2;1) = - ------------- 1/2 2 + 3 1/2 -1 - 3 3 3F2(1,3/2,1/6;11/6,2;1) = - ----------- 1/2 2 + 2 3 1/2 5 3 3F2(1,3/2,1/6;11/6,1;1) = ------ 4 1/2 -8 - 8 3 3F2(1,3/2,5/6;5/3,2;1) = - ----------- 1/2 3 + 2 3 1/2 3 3F2(1,3/2,5/6;5/3,1;1) = - ---- 3 1/2 -65 + 13 3 3F2(1,4/3,2/3;19/6,11/6;1) = - ------------- 1/2 18 + 9 3 1/2 13 91 3 3F2(1,4/3,2/3;19/6,5/6;1) = -- + ------- 45 90 1/2 -11 - 11 3 3F2(1,4/3,2/3;17/6,13/6;1) = - ------------- 1/2 12 + 7 3 1/2 11 55 3 3F2(1,4/3,2/3;17/6,7/6;1) = - -- + ------- 21 42 1/2 35 - 35 3 3F2(1,4/3,2/3;11/6,13/6;1) = - ------------ 1/2 6 + 6 3 1/2 35 - 35 3 3F2(1,4/3,2/3;13/6,11/6;1) = - ------------ 1/2 6 + 6 3 1/2 -128 - 160 3 3F2(1,7/6,1/2;3,7/3;1) = - --------------- 1/2 180 + 105 3 1/2 -20 + 4 3 3F2(1,7/6,1/2;3,11/6;1) = - ------------ 1/2 6 + 3 3 1/2 -40 - 48 3 3F2(1,7/6,1/2;3,4/3;1) = - ------------- 1/2 45 + 30 3 1/2 16 3 3F2(1,7/6,1/2;3,5/6;1) = - 4/15 + ------- 15 1/2 -253 + 66 3 3F2(1,7/6,1/2;17/6,2;1) = - -------------- 1/2 64 + 32 3 1/2 55 3 3F2(1,7/6,1/2;17/6,1;1) = ------- 64 1/2 16 - 48 3 3F2(1,7/6,5/6;8/3,7/3;1) = - ------------ 1/2 27 + 15 3 1/2 -4 - 12 3 3F2(1,7/6,5/6;8/3,4/3;1) = - ------------ 1/2 9 + 3 3 1/2 16 - 32 3 3F2(1,7/6,1/2;7/3,2;1) = - ------------ 1/2 15 + 10 3 1/2 16 3 3F2(1,7/6,1/2;7/3,1;1) = ------- 15 1/2 16 - 48 3 3F2(1,7/6,5/6;7/3,8/3;1) = - ------------ 1/2 27 + 15 3 1/2 32 - 32 3 3F2(1,7/6,5/6;7/3,5/3;1) = - ------------ 1/2 9 + 3 3 1/2 32 - 32 3 3F2(1,7/6,5/6;5/3,7/3;1) = - ------------ 1/2 9 + 3 3 5 3F2(1,7/6,1/2;11/6,2;1) = -------- 1/2 2 + 3 1/2 5 3 3F2(1,7/6,1/2;11/6,1;1) = ------ 2 1/2 16 - 32 3 3F2(1,7/6,1/2;2,7/3;1) = - ------------ 1/2 15 + 10 3 5 3F2(1,7/6,1/2;2,11/6;1) = -------- 1/2 2 + 3 1/2 1/2 (4 - 4 3 ) 3 3F2(1,7/6,1/2;2,4/3;1) = - ----------------- 3 1/2 -8 - 6 3 3F2(1,7/6,1/2;2,5/6;1) = - ----------- 1/2 2 + 3 1/2 1/2 (4 - 4 3 ) 3 3F2(1,7/6,1/2;4/3,2;1) = - ----------------- 3 1/2 3 3F2(1,7/6,1/2;4/3,1;1) = - ---- 3 1/2 -4 - 12 3 3F2(1,7/6,5/6;4/3,8/3;1) = - ------------ 1/2 9 + 3 3 1/2 -176 - 32 3 3F2(1,1/2,1/6;7/3,2;1) = - -------------- 1/2 105 + 70 3 1/2 64 3 3F2(1,1/2,1/6;7/3,1;1) = ------- 105 1/2 7 3 3F2(1,1/2,1/6;2,11/6;1) = -2 + ------ 4 1/2 1/2 (-16 + 4 3 ) 3 3F2(1,1/2,1/6;2,4/3;1) = - ------------------- 15 1/2 1/2 (6 + 2 3 ) 3 3F2(1,1/2,1/6;2,5/6;1) = ----------------- 15 1/2 1/2 (2 - 8 3 ) 3 3F2(1,1/2,1/6;2,1/3;1) = - ----------------- 15 1/2 7 3 3F2(1,1/2,1/6;11/6,2;1) = -2 + ------ 4 1/2 5 3 3F2(1,1/2,1/6;11/6,1;1) = ------ 8 1/2 5 3 3F2(1,1/2,1/6;1,11/6;1) = ------ 8 1/2 2 3 3F2(1,1/2,1/6;1,4/3;1) = ------ 3 1/2 3F2(1,1/2,1/6;1,5/6;1) = 3 1/2 3 3F2(1,1/2,1/6;1,1/3;1) = ---- 6 1/2 1/2 (-16 + 4 3 ) 3 3F2(1,1/2,1/6;4/3,2;1) = - ------------------- 15 1/2 2 3 3F2(1,1/2,1/6;4/3,1;1) = ------ 3 1/2 1/2 (6 + 2 3 ) 3 3F2(1,1/2,1/6;5/6,2;1) = ----------------- 15 1/2 3F2(1,1/2,1/6;5/6,1;1) = 3 7 3F2(1,2/3,1/3;13/6,11/6;1) = ---------- 1/2 3 + 2 3 1/2 7 3 3F2(1,2/3,1/3;13/6,5/6;1) = 7/15 + ------ 15 7 3F2(1,2/3,1/3;11/6,13/6;1) = ---------- 1/2 3 + 2 3 1/2 5 3 3F2(1,2/3,1/3;11/6,7/6;1) = - 5/3 + ------ 3 1/2 5 3 3F2(1,2/3,1/3;7/6,11/6;1) = - 5/3 + ------ 3 1/2 7 3 3F2(1,2/3,1/3;5/6,13/6;1) = 7/15 + ------ 15 1/2 112 + 44 3 3F2(1,5/6,1/2;8/3,2;1) = - ------------- 1/2 -84 - 49 3 1/2 16 3 3F2(1,5/6,1/2;8/3,1;1) = ------- 21 1/2 20 + 24 3 3F2(1,5/6,1/6;8/3,4/3;1) = - ------------- 1/2 -27 - 18 3 1/2 1/2 (8 + 8 3 ) 3 3F2(1,5/6,1/6;8/3,1/3;1) = ----------------- 27 1/2 -32 - 64 3 3F2(1,5/6,1/6;7/3,5/3;1) = - ------------- 1/2 63 + 42 3 1/2 1/2 (16 + 16 3 ) 3 3F2(1,5/6,1/6;7/3,2/3;1) = ------------------- 63 1/2 28 + 21 3 3F2(1,5/6,1/2;13/6,2;1) = - ------------- 1/2 -28 - 16 3 1/2 7 3 3F2(1,5/6,1/2;13/6,1;1) = ------ 8 1/2 28 + 21 3 3F2(1,5/6,1/2;2,13/6;1) = - ------------- 1/2 -28 - 16 3 8 3F2(1,5/6,1/2;2,5/3;1) = ---------- 1/2 3 + 2 3 1/2 4 3 3F2(1,5/6,1/2;2,7/6;1) = -------- 1/2 3 + 3 1/2 1/2 (2 - 4 3 ) 3 3F2(1,5/6,1/2;2,2/3;1) = - ----------------- 3 1/2 1/2 (8 - 8 3 ) 3 3F2(1,5/6,1/6;4/3,5/3;1) = - ----------------- 9 8 3F2(1,5/6,1/2;5/3,2;1) = ---------- 1/2 3 + 2 3 1/2 4 3 3F2(1,5/6,1/2;5/3,1;1) = ------ 3 1/2 1/2 (8 - 8 3 ) 3 3F2(1,5/6,1/6;5/3,4/3;1) = - ----------------- 9 1/2 4 3 3F2(1,5/6,1/2;7/6,2;1) = -------- 1/2 3 + 3 1/2 3F2(1,5/6,1/2;7/6,1;1) = -3 1/2 7 3 3F2(1,5/6,1/2;1,13/6;1) = ------ 8 1/2 4 3 3F2(1,5/6,1/2;1,5/3;1) = ------ 3 1/2 3F2(1,5/6,1/2;1,7/6;1) = -3 1/2 3 3F2(1,5/6,1/2;1,2/3;1) = ---- 12 The following bunch of evaluations feature the square of the cubic root of 2\ , i.e. 2^(2/3) They are probably equivalent to each other (1/3) 2/3 (-1944 + 1536 2 ) 2 3F2(1,11/6,4/3;11/3,3;1) = - -------------------------- 10 (1/3) 2/3 (648 - 522 2 ) 2 3F2(1,11/6,4/3;11/3,5/2;1) = - ----------------------- 10 (1/3) 2/3 (-72 + 48 2 ) 2 3F2(1,11/6,4/3;11/3,2;1) = - ---------------------- 10 (1/3) 2/3 (-24 + 6 2 ) 2 3F2(1,11/6,4/3;11/3,3/2;1) = - --------------------- 10 (1/3) 2/3 (162 - 168 2 ) 2 3F2(1,11/6,1/3;11/3,2;1) = - ----------------------- 70 (1/3) 2/3 (144 - 156 2 ) 2 3F2(1,11/6,1/3;11/3,3/2;1) = - ----------------------- 70 2/3 6 2 3F2(1,11/6,1/3;11/3,1;1) = ------ 7 (1/3) 2/3 (64 + 24 2 ) 2 3F2(1,11/6,1/3;11/3,1/2;1) = --------------------- 70 1/3 1458 2 3F2(1,11/6,4/3;7/2,3;1) = -261 + --------- 7 (1/3) 2/3 (1215 - 975 2 ) 2 3F2(1,11/6,4/3;7/2,8/3;1) = - ------------------------ 14 1/3 243 2 3F2(1,11/6,4/3;7/2,2;1) = -9 + -------- 28 (1/3) 2/3 (-81 + 30 2 ) 2 3F2(1,11/6,4/3;7/2,5/3;1) = - ---------------------- 28 1/3 243 2 3F2(1,11/6,1/3;7/2,2;1) = 9/2 - -------- 91 (1/3) 2/3 (243 - 300 2 ) 2 3F2(1,11/6,1/3;7/2,5/3;1) = - ----------------------- 182 1/3 405 2 3F2(1,11/6,1/3;7/2,1;1) = -------- 364 (1/3) 2/3 (81 + 30 2 ) 2 3F2(1,11/6,1/3;7/2,2/3;1) = --------------------- 104 (1/3) 3F2(1,11/6,5/3;10/3,3;1) = -210 + 168 2 1/3 28 2 3F2(1,11/6,5/3;10/3,2;1) = - 21/5 + ------- 5 1/3 28 2 3F2(1,11/6,2/3;10/3,2;1) = 42/5 - ------- 5 1/3 28 2 3F2(1,11/6,2/3;10/3,1;1) = ------- 15 (1/3) 2/3 (-1092 + 858 2 ) 2 3F2(1,11/6,5/3;19/6,3;1) = - ------------------------- 10 (1/3) 2/3 (-91 + 39 2 ) 2 3F2(1,11/6,5/3;19/6,2;1) = - ---------------------- 20 (1/3) 2/3 (364 - 351 2 ) 2 3F2(1,11/6,2/3;19/6,2;1) = - ----------------------- 90 2/3 91 2 3F2(1,11/6,2/3;19/6,1;1) = ------- 54 (1/3) 3F2(1,11/6,5/3;3,10/3;1) = -210 + 168 2 (1/3) 2/3 (-1092 + 858 2 ) 2 3F2(1,11/6,5/3;3,19/6;1) = - ------------------------- 10 (1/3) 2/3 (-126 + 84 2 ) 2 3F2(1,11/6,5/3;3,13/6;1) = - ----------------------- 10 1/3 144 2 3F2(1,11/6,5/3;3,7/3;1) = - 168/5 + -------- 5 (1/3) 2/3 (-108 + 84 2 ) 2 3F2(1,11/6,4/3;3,8/3;1) = - ----------------------- 2 1/3 243 2 3F2(1,11/6,4/3;3,5/2;1) = - 297/5 + -------- 5 (1/3) 2/3 (36 - 48 2 ) 2 3F2(1,11/6,4/3;3,5/3;1) = - --------------------- 10 1/3 27 2 3F2(1,11/6,4/3;3,3/2;1) = 63/5 - ------- 5 (1/3) 3F2(1,11/6,2/3;3,7/3;1) = 24 - 18 2 (1/3) 2/3 (168 - 147 2 ) 2 3F2(1,11/6,2/3;3,13/6;1) = - ----------------------- 20 (1/3) 2/3 (-72 + 33 2 ) 2 3F2(1,11/6,2/3;3,7/6;1) = - ---------------------- 20 1/3 27 2 3F2(1,11/6,2/3;3,4/3;1) = - 24/5 + ------- 5 (1/3) 2/3 (-54 + 12 2 ) 2 3F2(1,11/6,1/3;3,5/3;1) = - ---------------------- 50 1/3 36 54 2 3F2(1,11/6,1/3;3,3/2;1) = - -- + ------- 25 25 (1/3) 2/3 (63 - 114 2 ) 2 3F2(1,11/6,1/3;3,2/3;1) = - ---------------------- 50 1/3 198 72 2 3F2(1,11/6,1/3;3,1/2;1) = --- - ------- 25 25 1/3 144 2 3F2(1,11/6,5/3;7/3,3;1) = - 168/5 + -------- 5 1/3 24 2 3F2(1,11/6,5/3;7/3,2;1) = - 12/5 - ------- 5 1/3 12 2 3F2(1,11/6,2/3;7/3,2;1) = 24/5 - ------- 5 (1/3) 3F2(1,11/6,2/3;7/3,1;1) = -4 2 1/3 243 2 3F2(1,11/6,4/3;5/2,3;1) = - 297/5 + -------- 5 (1/3) 2/3 (54 - 45 2 ) 2 3F2(1,11/6,4/3;5/2,8/3;1) = - --------------------- 2 1/3 81 2 3F2(1,11/6,4/3;5/2,2;1) = - 27/5 + ------- 10 1/3 27 81 2 3F2(1,11/6,1/3;5/2,2;1) = -- - ------- 10 70 (1/3) 2/3 (54 - 90 2 ) 2 3F2(1,11/6,1/3;5/2,5/3;1) = - --------------------- 70 1/3 27 2 3F2(1,11/6,1/3;5/2,1;1) = ------- 14 (1/3) 2/3 (-108 + 84 2 ) 2 3F2(1,11/6,4/3;8/3,3;1) = - ----------------------- 2 (1/3) 2/3 (54 - 45 2 ) 2 3F2(1,11/6,4/3;8/3,5/2;1) = - --------------------- 2 (1/3) 2/3 (-12 + 6 2 ) 2 3F2(1,11/6,4/3;8/3,2;1) = - --------------------- 2 (1/3) 2/3 (9 - 12 2 ) 2 3F2(1,11/6,1/3;8/3,2;1) = - -------------------- 8 (1/3) 2/3 (12 - 15 2 ) 2 3F2(1,11/6,1/3;8/3,3/2;1) = - --------------------- 8 2/3 5 2 3F2(1,11/6,1/3;8/3,1;1) = ------ 4 (1/3) 2/3 (-126 + 84 2 ) 2 3F2(1,11/6,5/3;13/6,3;1) = - ----------------------- 10 (1/3) 2/3 (21 + 21 2 ) 2 3F2(1,11/6,5/3;13/6,2;1) = - --------------------- 20 (1/3) 2/3 (14 - 21 2 ) 2 3F2(1,11/6,2/3;13/6,2;1) = - --------------------- 10 2/3 7 2 3F2(1,11/6,2/3;13/6,1;1) = - ------ 6 1/3 28 2 3F2(1,11/6,5/3;2,10/3;1) = - 21/5 + ------- 5 (1/3) 2/3 (-91 + 39 2 ) 2 3F2(1,11/6,5/3;2,19/6;1) = - ---------------------- 20 (1/3) 2/3 (21 + 21 2 ) 2 3F2(1,11/6,5/3;2,13/6;1) = - --------------------- 20 1/3 24 2 3F2(1,11/6,5/3;2,7/3;1) = - 12/5 - ------- 5 (1/3) 2/3 (-12 + 6 2 ) 2 3F2(1,11/6,4/3;2,8/3;1) = - --------------------- 2 1/3 81 2 3F2(1,11/6,4/3;2,5/2;1) = - 27/5 + ------- 10 (1/3) 2/3 (-4 + 12 2 ) 2 3F2(1,11/6,4/3;2,5/3;1) = - --------------------- 10 1/3 9 2 3F2(1,11/6,4/3;2,3/2;1) = - 9/5 + ------ 20 1/3 12 2 3F2(1,11/6,2/3;2,7/3;1) = 24/5 - ------- 5 (1/3) 2/3 (14 - 21 2 ) 2 3F2(1,11/6,2/3;2,13/6;1) = - --------------------- 10 (1/3) 2/3 (12 - 3 2 ) 2 3F2(1,11/6,2/3;2,7/6;1) = - -------------------- 10 1/3 18 2 3F2(1,11/6,2/3;2,4/3;1) = 6/5 - ------- 5 (1/3) 2/3 (3 + 6 2 ) 2 3F2(1,11/6,1/3;2,5/3;1) = ------------------- 10 1/3 9 2 3F2(1,11/6,1/3;2,3/2;1) = 9/10 + ------ 10 (1/3) 2/3 (-7 + 6 2 ) 2 3F2(1,11/6,1/3;2,2/3;1) = - -------------------- 20 1/3 3 2 3F2(1,11/6,1/3;2,1/2;1) = - 9/10 + ------ 5 (1/3) 2/3 (-729 + 576 2 ) 2 3F2(1,5/3,7/6;7/2,3;1) = - ------------------------ 4 1/3 243 2 3F2(1,5/3,7/6;7/2,7/3;1) = 78 - -------- 4 (1/3) 2/3 (-243 + 180 2 ) 2 3F2(1,5/3,7/6;7/2,2;1) = - ------------------------ 16 1/3 81 2 3F2(1,5/3,7/6;7/2,4/3;1) = - 3/4 + ------- 32 (1/3) 2/3 (243 - 252 2 ) 2 3F2(1,5/3,1/6;7/2,2;1) = - ----------------------- 112 1/3 69 243 2 3F2(1,5/3,1/6;7/2,4/3;1) = -- - -------- 28 224 2/3 81 2 3F2(1,5/3,1/6;7/2,1;1) = ------- 112 1/3 81 2 3F2(1,5/3,1/6;7/2,1/3;1) = 6/7 + ------- 112 (1/3) 3F2(1,5/3,3/2;10/3,17/6;1) = - 385/2 + 154 2 1/3 14 2 3F2(1,5/3,3/2;10/3,11/6;1) = - 7/2 + ------- 3 1/3 972 2 3F2(1,5/3,7/6;10/3,3;1) = - 1218/5 + -------- 5 (1/3) 3F2(1,5/3,7/6;10/3,5/2;1) = 207/2 - 81 2 (1/3) 3F2(1,5/3,7/6;10/3,2;1) = -21 + 18 2 (1/3) 3F2(1,5/3,7/6;10/3,3/2;1) = - 3/2 + 3 2 1/3 133 42 2 3F2(1,5/3,1/2;10/3,11/6;1) = --- - ------- 22 11 1/3 14 2 3F2(1,5/3,1/2;10/3,5/6;1) = 7/22 + ------- 11 1/3 140 2 3F2(1,5/3,5/6;10/3,2;1) = 21 - -------- 9 1/3 56 2 3F2(1,5/3,5/6;10/3,1;1) = ------- 27 1/3 162 2 3F2(1,5/3,1/6;10/3,2;1) = 21/5 - -------- 65 1/3 51 9 2 3F2(1,5/3,1/6;10/3,3/2;1) = -- - ------ 26 13 1/3 12 2 3F2(1,5/3,1/6;10/3,1;1) = ------- 13 1/3 21 7 2 3F2(1,5/3,1/6;10/3,1/2;1) = -- + ------ 26 13 (1/3) 2/3 (91 - 78 2 ) 2 3F2(1,5/3,5/6;19/6,2;1) = - --------------------- 8 2/3 91 2 3F2(1,5/3,5/6;19/6,1;1) = ------- 48 (1/3) 2/3 (-486 + 378 2 ) 2 3F2(1,5/3,7/6;3,5/2;1) = - ------------------------ 10 1/3 216 2 3F2(1,5/3,7/6;3,7/3;1) = - 264/5 + -------- 5 (1/3) 2/3 (27 - 36 2 ) 2 3F2(1,5/3,7/6;3,3/2;1) = - --------------------- 10 1/3 18 2 3F2(1,5/3,7/6;3,4/3;1) = 42/5 - ------- 5 1/3 240 2 3F2(1,5/3,5/6;3,7/3;1) = 312/7 - -------- 7 (1/3) 2/3 (36 - 30 2 ) 2 3F2(1,5/3,5/6;3,13/6;1) = - --------------------- 2 1/3 36 2 3F2(1,5/3,5/6;3,4/3;1) = - 30/7 + ------- 7 (1/3) 2/3 (-54 + 24 2 ) 2 3F2(1,5/3,5/6;3,7/6;1) = - ---------------------- 14 (1/3) 2/3 (54 + 18 2 ) 2 3F2(1,5/3,1/6;3,3/2;1) = --------------------- 110 1/3 54 2 3F2(1,5/3,1/6;3,4/3;1) = - 6/55 + ------- 55 (1/3) 2/3 (63 - 144 2 ) 2 3F2(1,5/3,1/6;3,1/2;1) = - ---------------------- 110 1/3 228 72 2 3F2(1,5/3,1/6;3,1/3;1) = --- - ------- 55 55 (1/3) 3F2(1,5/3,3/2;17/6,10/3;1) = - 385/2 + 154 2 1/3 110 2 3F2(1,5/3,3/2;17/6,7/3;1) = -44 + -------- 3 1/3 33 2 3F2(1,5/3,1/2;17/6,7/3;1) = 22 - ------- 2 1/3 55 2 3F2(1,5/3,1/2;17/6,4/3;1) = - 11/4 + ------- 16 (1/3) 2/3 (21 - 21 2 ) 2 3F2(1,5/3,5/6;13/6,2;1) = - --------------------- 4 2/3 7 2 3F2(1,5/3,5/6;13/6,1;1) = - ------ 4 1/3 110 2 3F2(1,5/3,3/2;7/3,17/6;1) = -44 + -------- 3 1/3 216 2 3F2(1,5/3,7/6;7/3,3;1) = - 264/5 + -------- 5 (1/3) 3F2(1,5/3,7/6;7/3,5/2;1) = 36 - 27 2 (1/3) 3F2(1,5/3,7/6;7/3,2;1) = -12 + 12 2 (1/3) 3F2(1,5/3,1/2;7/3,11/6;1) = 4 - 2 2 (1/3) 3F2(1,5/3,5/6;7/3,2;1) = 12 - 8 2 1/3 16 2 3F2(1,5/3,5/6;7/3,1;1) = - ------- 3 1/3 36 2 3F2(1,5/3,1/6;7/3,2;1) = 12/5 - ------- 35 1/3 3 2 3F2(1,5/3,1/6;7/3,3/2;1) = 12/7 - ------ 7 1/3 8 2 3F2(1,5/3,1/6;7/3,1;1) = ------ 7 (1/3) 2/3 (-486 + 378 2 ) 2 3F2(1,5/3,7/6;5/2,3;1) = - ------------------------ 10 (1/3) 3F2(1,5/3,7/6;5/2,7/3;1) = 36 - 27 2 (1/3) 2/3 (-81 + 54 2 ) 2 3F2(1,5/3,7/6;5/2,2;1) = - ---------------------- 8 (1/3) 2/3 (81 - 108 2 ) 2 3F2(1,5/3,1/6;5/2,2;1) = - ---------------------- 80 1/3 27 2 3F2(1,5/3,1/6;5/2,4/3;1) = 9/4 - ------- 32 2/3 27 2 3F2(1,5/3,1/6;5/2,1;1) = ------- 32 (1/3) 2/3 (-81 + 54 2 ) 2 3F2(1,5/3,7/6;2,5/2;1) = - ---------------------- 8 (1/3) 3F2(1,5/3,7/6;2,7/3;1) = -12 + 12 2 (1/3) 2/3 (-9 + 18 2 ) 2 3F2(1,5/3,7/6;2,3/2;1) = - --------------------- 8 (1/3) 3F2(1,5/3,7/6;2,4/3;1) = -3 + 2 (1/3) 3F2(1,5/3,5/6;2,7/3;1) = 12 - 8 2 (1/3) 2/3 (21 - 21 2 ) 2 3F2(1,5/3,5/6;2,13/6;1) = - --------------------- 4 (1/3) 3F2(1,5/3,5/6;2,4/3;1) = 3 - 6 2 (1/3) 2/3 (9 - 3 2 ) 2 3F2(1,5/3,5/6;2,7/6;1) = - ------------------- 4 (1/3) 2/3 (9 + 18 2 ) 2 3F2(1,5/3,1/6;2,3/2;1) = -------------------- 40 1/3 3 2 3F2(1,5/3,1/6;2,4/3;1) = 3/5 + ------ 5 (1/3) 2/3 (-21 + 18 2 ) 2 3F2(1,5/3,1/6;2,1/2;1) = - ---------------------- 40 1/3 4 2 3F2(1,5/3,1/6;2,1/3;1) = - 6/5 + ------ 5 1/3 14 2 3F2(1,5/3,3/2;11/6,10/3;1) = - 7/2 + ------- 3 (1/3) 3F2(1,5/3,1/2;11/6,7/3;1) = 4 - 2 2 1/3 56 2 3F2(1,3/2,2/3;10/3,11/6;1) = 77/5 - ------- 5 1/3 112 2 3F2(1,3/2,2/3;10/3,5/6;1) = 7/25 + -------- 75 (1/3) 2/3 (-182 + 143 2 ) 2 3F2(1,3/2,4/3;19/6,8/3;1) = - ------------------------ 2 (1/3) 2/3 (-91 + 39 2 ) 2 3F2(1,3/2,4/3;19/6,5/3;1) = - ---------------------- 30 (1/3) 2/3 (182 - 208 2 ) 2 3F2(1,3/2,1/3;19/6,5/3;1) = - ----------------------- 110 (1/3) 2/3 (91 + 39 2 ) 2 3F2(1,3/2,1/3;19/6,2/3;1) = --------------------- 132 1/3 220 2 3F2(1,3/2,2/3;17/6,7/3;1) = 286/7 - -------- 7 1/3 55 2 3F2(1,3/2,2/3;17/6,4/3;1) = - 11/7 + ------- 21 (1/3) 2/3 (-182 + 143 2 ) 2 3F2(1,3/2,4/3;8/3,19/6;1) = - ------------------------ 2 (1/3) 2/3 (-140 + 105 2 ) 2 3F2(1,3/2,4/3;8/3,13/6;1) = - ------------------------ 6 (1/3) 2/3 (56 - 49 2 ) 2 3F2(1,3/2,1/3;8/3,13/6;1) = - --------------------- 8 (1/3) 2/3 (-40 + 15 2 ) 2 3F2(1,3/2,1/3;8/3,7/6;1) = - ---------------------- 24 (1/3) 2/3 (-140 + 105 2 ) 2 3F2(1,3/2,4/3;13/6,8/3;1) = - ------------------------ 6 (1/3) 2/3 (28 - 42 2 ) 2 3F2(1,3/2,1/3;13/6,5/3;1) = - --------------------- 30 1/3 20 2 3F2(1,3/2,2/3;7/3,11/6;1) = 10 - ------- 3 1/3 20 2 3F2(1,3/2,2/3;11/6,7/3;1) = 10 - ------- 3 (1/3) 2/3 (-91 + 39 2 ) 2 3F2(1,3/2,4/3;5/3,19/6;1) = - ---------------------- 30 (1/3) 2/3 (28 - 42 2 ) 2 3F2(1,3/2,1/3;5/3,13/6;1) = - --------------------- 30 (1/3) 2/3 (273 - 247 2 ) 2 3F2(1,4/3,1/2;19/6,5/3;1) = - ----------------------- 50 (1/3) 2/3 (91 + 26 2 ) 2 3F2(1,4/3,1/2;19/6,2/3;1) = --------------------- 100 (1/3) 3F2(1,4/3,7/6;3,17/6;1) = -165 + 132 2 (1/3) 2/3 (-168 + 132 2 ) 2 3F2(1,4/3,7/6;3,8/3;1) = - ------------------------ 2 (1/3) 2/3 (-72 + 48 2 ) 2 3F2(1,4/3,7/6;3,5/3;1) = - ---------------------- 10 (1/3) 3F2(1,4/3,7/6;3,11/6;1) = -21 + 18 2 (1/3) 2/3 (972 - 780 2 ) 2 3F2(1,4/3,5/6;3,8/3;1) = - ----------------------- 14 1/3 486 2 3F2(1,4/3,5/6;3,5/2;1) = 621/7 - -------- 7 1/3 27 2 3F2(1,4/3,5/6;3,3/2;1) = 45/7 - ------- 7 (1/3) 2/3 (108 - 96 2 ) 2 3F2(1,4/3,5/6;3,5/3;1) = - ---------------------- 14 1/3 57 36 2 3F2(1,4/3,1/6;3,11/6;1) = -- - ------- 11 11 (1/3) 2/3 (168 - 192 2 ) 2 3F2(1,4/3,1/6;3,5/3;1) = - ----------------------- 110 (1/3) 2/3 (72 + 12 2 ) 2 3F2(1,4/3,1/6;3,2/3;1) = --------------------- 110 1/3 54 2 3F2(1,4/3,1/6;3,5/6;1) = - 3/55 + ------- 55 (1/3) 3F2(1,4/3,7/6;17/6,3;1) = -165 + 132 2 1/3 55 2 3F2(1,4/3,7/6;17/6,2;1) = -33 + ------- 2 1/3 22 2 3F2(1,4/3,1/6;17/6,2;1) = 33/5 - ------- 5 1/3 11 2 3F2(1,4/3,1/6;17/6,1;1) = ------- 12 (1/3) 2/3 (-168 + 132 2 ) 2 3F2(1,4/3,7/6;8/3,3;1) = - ------------------------ 2 (1/3) 2/3 (-40 + 30 2 ) 2 3F2(1,4/3,7/6;8/3,2;1) = - ---------------------- 2 (1/3) 2/3 (30 - 25 2 ) 2 3F2(1,4/3,1/2;8/3,13/6;1) = - --------------------- 2 (1/3) 2/3 (-20 + 5 2 ) 2 3F2(1,4/3,1/2;8/3,7/6;1) = - --------------------- 14 (1/3) 2/3 (-81 + 63 2 ) 2 3F2(1,4/3,5/6;8/3,5/2;1) = - ---------------------- 2 (1/3) 2/3 (36 - 30 2 ) 2 3F2(1,4/3,5/6;8/3,2;1) = - --------------------- 2 (1/3) 2/3 (-6 + 3 2 ) 2 3F2(1,4/3,5/6;8/3,3/2;1) = - -------------------- 2 (2/3) 3F2(1,4/3,5/6;8/3,1;1) = 2 2 (1/3) 2/3 (56 - 54 2 ) 2 3F2(1,4/3,1/6;8/3,2;1) = - --------------------- 18 2/3 20 2 3F2(1,4/3,1/6;8/3,1;1) = ------- 27 (1/3) 2/3 (-81 + 63 2 ) 2 3F2(1,4/3,5/6;5/2,8/3;1) = - ---------------------- 2 1/3 81 2 3F2(1,4/3,5/6;5/2,2;1) = 27 - ------- 4 (1/3) 2/3 (-27 + 18 2 ) 2 3F2(1,4/3,5/6;5/2,5/3;1) = - ---------------------- 4 1/3 27 2 3F2(1,4/3,5/6;5/2,1;1) = ------- 8 (1/3) 3F2(1,4/3,7/6;11/6,3;1) = -21 + 18 2 (1/3) 3F2(1,4/3,7/6;11/6,2;1) = -15 + 15 2 1/3 3 2 3F2(1,4/3,1/6;11/6,2;1) = 3 - ------ 2 1/3 5 2 3F2(1,4/3,1/6;11/6,1;1) = ------ 4 1/3 55 2 3F2(1,4/3,7/6;2,17/6;1) = -33 + ------- 2 (1/3) 2/3 (-40 + 30 2 ) 2 3F2(1,4/3,7/6;2,8/3;1) = - ---------------------- 2 (1/3) 2/3 (-24 + 12 2 ) 2 3F2(1,4/3,7/6;2,5/3;1) = - ---------------------- 2 (1/3) 3F2(1,4/3,7/6;2,11/6;1) = -15 + 15 2 (1/3) 2/3 (36 - 30 2 ) 2 3F2(1,4/3,5/6;2,8/3;1) = - --------------------- 2 1/3 81 2 3F2(1,4/3,5/6;2,5/2;1) = 27 - ------- 4 1/3 9 2 3F2(1,4/3,5/6;2,3/2;1) = 9 - ------ 2 (1/3) 2/3 (12 - 12 2 ) 2 3F2(1,4/3,5/6;2,5/3;1) = - --------------------- 2 1/3 3 2 3F2(1,4/3,1/6;2,11/6;1) = 3 - ------ 2 (1/3) 2/3 (8 - 12 2 ) 2 3F2(1,4/3,1/6;2,5/3;1) = - -------------------- 10 (1/3) 2/3 (-24 + 6 2 ) 2 3F2(1,4/3,1/6;2,2/3;1) = - --------------------- 10 1/3 9 2 3F2(1,4/3,1/6;2,5/6;1) = - 3/5 + ------ 5 (1/3) 2/3 (7 - 7 2 ) 2 3F2(1,4/3,1/2;13/6,5/3;1) = - ------------------- 2 (1/3) 2/3 (-72 + 48 2 ) 2 3F2(1,4/3,7/6;5/3,3;1) = - ---------------------- 10 (1/3) 2/3 (-24 + 12 2 ) 2 3F2(1,4/3,7/6;5/3,2;1) = - ---------------------- 2 (1/3) 2/3 (7 - 7 2 ) 2 3F2(1,4/3,1/2;5/3,13/6;1) = - ------------------- 2 (1/3) 2/3 (-27 + 18 2 ) 2 3F2(1,4/3,5/6;5/3,5/2;1) = - ---------------------- 4 (1/3) 2/3 (12 - 12 2 ) 2 3F2(1,4/3,5/6;5/3,2;1) = - --------------------- 2 2/3 2 2 3F2(1,4/3,5/6;5/3,1;1) = - ------ 3 (1/3) 2/3 (8 - 12 2 ) 2 3F2(1,4/3,1/6;5/3,2;1) = - -------------------- 10 2/3 4 2 3F2(1,4/3,1/6;5/3,1;1) = ------ 3 (1/3) 2/3 (-6 + 3 2 ) 2 3F2(1,4/3,5/6;3/2,8/3;1) = - -------------------- 2 1/3 9 2 3F2(1,4/3,5/6;3/2,2;1) = 9 - ------ 2 1/3 3 2 3F2(1,4/3,5/6;3/2,1;1) = - ------ 8 (1/3) 2/3 (972 - 783 2 ) 2 3F2(1,7/6,2/3;3,5/2;1) = - ----------------------- 20 1/3 243 2 3F2(1,7/6,2/3;3,7/3;1) = 312/5 - -------- 5 1/3 27 2 3F2(1,7/6,2/3;3,4/3;1) = 24/5 - ------- 10 (1/3) 2/3 (108 - 99 2 ) 2 3F2(1,7/6,2/3;3,3/2;1) = - ---------------------- 20 1/3 48 2 3F2(1,7/6,1/3;3,11/6;1) = 66/5 - ------- 5 (1/3) 2/3 (252 - 228 2 ) 2 3F2(1,7/6,1/3;3,5/3;1) = - ----------------------- 50 1/3 12 36 2 3F2(1,7/6,1/3;3,5/6;1) = - -- + ------- 25 25 (1/3) 2/3 (-54 + 6 2 ) 2 3F2(1,7/6,1/3;3,2/3;1) = - --------------------- 50 1/3 110 2 3F2(1,7/6,1/3;17/6,2;1) = 33/2 - -------- 9 1/3 55 2 3F2(1,7/6,1/3;17/6,1;1) = ------- 54 (1/3) 2/3 (35 - 30 2 ) 2 3F2(1,7/6,1/3;8/3,2;1) = - --------------------- 4 2/3 5 2 3F2(1,7/6,1/3;8/3,1;1) = ------ 6 1/3 162 2 3F2(1,7/6,2/3;5/2,7/3;1) = - 198/5 + -------- 5 (1/3) 2/3 (162 - 135 2 ) 2 3F2(1,7/6,2/3;5/2,2;1) = - ----------------------- 10 1/3 27 2 3F2(1,7/6,2/3;5/2,4/3;1) = - 9/5 + ------- 10 2/3 27 2 3F2(1,7/6,2/3;5/2,1;1) = ------- 20 1/3 162 2 3F2(1,7/6,2/3;7/3,5/2;1) = - 198/5 + -------- 5 (1/3) 3F2(1,7/6,2/3;7/3,2;1) = 24 - 18 2 (1/3) 3F2(1,7/6,2/3;7/3,3/2;1) = -6 + 6 2 (1/3) 3F2(1,7/6,2/3;7/3,1;1) = 2 2 (1/3) 2/3 (6 - 6 2 ) 2 3F2(1,7/6,1/3;5/3,2;1) = - ------------------- 2 (2/3) 3F2(1,7/6,1/3;5/3,1;1) = 2 2 (1/3) 3F2(1,7/6,1/3;11/6,2;1) = 15/2 - 5 2 1/3 5 2 3F2(1,7/6,1/3;11/6,1;1) = ------ 3 (1/3) 2/3 (162 - 135 2 ) 2 3F2(1,7/6,2/3;2,5/2;1) = - ----------------------- 10 (1/3) 3F2(1,7/6,2/3;2,7/3;1) = 24 - 18 2 (1/3) 3F2(1,7/6,2/3;2,4/3;1) = 6 - 3 2 (1/3) 2/3 (9 - 9 2 ) 2 3F2(1,7/6,2/3;2,3/2;1) = - ------------------- 2 (1/3) 3F2(1,7/6,1/3;2,11/6;1) = 15/2 - 5 2 (1/3) 2/3 (6 - 6 2 ) 2 3F2(1,7/6,1/3;2,5/3;1) = - ------------------- 2 (1/3) 3F2(1,7/6,1/3;2,5/6;1) = - 3/2 + 3 2 (1/3) 2/3 (-9 + 3 2 ) 2 3F2(1,7/6,1/3;2,2/3;1) = - -------------------- 2 (1/3) 3F2(1,7/6,2/3;3/2,7/3;1) = -6 + 6 2 (1/3) 2/3 (9 - 9 2 ) 2 3F2(1,7/6,2/3;3/2,2;1) = - ------------------- 2 2/3 3 2 3F2(1,7/6,2/3;3/2,1;1) = - ------ 4 1/3 27 2 3F2(1,7/6,2/3;4/3,5/2;1) = - 9/5 + ------- 10 (1/3) 3F2(1,7/6,2/3;4/3,2;1) = 6 - 3 2 1/3 2 3F2(1,7/6,2/3;4/3,1;1) = - ---- 3 (1/3) 2/3 (-42 + 28 2 ) 2 3F2(1,1/2,1/3;13/6,5/3;1) = - ---------------------- 10 (1/3) 2/3 (7 + 7 2 ) 2 3F2(1,1/2,1/3;13/6,2/3;1) = ------------------- 20 (1/3) 2/3 (-42 + 28 2 ) 2 3F2(1,1/2,1/3;5/3,13/6;1) = - ---------------------- 10 (1/3) 2/3 (-4 + 2 2 ) 2 3F2(1,1/2,1/3;5/3,7/6;1) = - -------------------- 2 (1/3) 2/3 (-4 + 2 2 ) 2 3F2(1,1/2,1/3;7/6,5/3;1) = - -------------------- 2 (1/3) 2/3 (7 + 7 2 ) 2 3F2(1,1/2,1/3;2/3,13/6;1) = ------------------- 20 (1/3) 2/3 (-81 + 54 2 ) 2 3F2(1,2/3,1/6;5/2,2;1) = - ---------------------- 20 1/3 81 2 3F2(1,2/3,1/6;5/2,4/3;1) = 18/5 - ------- 40 2/3 27 2 3F2(1,2/3,1/6;5/2,1;1) = ------- 40 1/3 27 2 3F2(1,2/3,1/6;5/2,1/3;1) = 9/10 + ------- 80 (1/3) 3F2(1,2/3,1/2;7/3,11/6;1) = -14 + 12 2 1/3 4 2 3F2(1,2/3,1/2;7/3,5/6;1) = 2/5 + ------ 5 1/3 162 2 3F2(1,2/3,1/6;7/3,2;1) = - 24/5 + -------- 35 1/3 18 2 3F2(1,2/3,1/6;7/3,3/2;1) = 30/7 - ------- 7 1/3 6 2 3F2(1,2/3,1/6;7/3,1;1) = ------ 7 1/3 2 2 3F2(1,2/3,1/6;7/3,1/2;1) = 6/7 + ------ 7 (1/3) 2/3 (-18 + 9 2 ) 2 3F2(1,2/3,1/6;2,3/2;1) = - --------------------- 10 1/3 9 2 3F2(1,2/3,1/6;2,4/3;1) = - 6/5 + ------ 5 (1/3) 2/3 (3 - 9 2 ) 2 3F2(1,2/3,1/6;2,1/2;1) = - ------------------- 10 1/3 3 2 3F2(1,2/3,1/6;2,1/3;1) = 12/5 - ------ 5 (1/3) 3F2(1,2/3,1/2;11/6,7/3;1) = -14 + 12 2 (1/3) 3F2(1,2/3,1/2;11/6,4/3;1) = -5 + 5 2 (1/3) 3F2(1,2/3,1/2;4/3,11/6;1) = -5 + 5 2 1/3 9 2 3F2(1,2/3,1/6;4/3,2;1) = - 6/5 + ------ 5 1/3 3 2 3F2(1,2/3,1/6;4/3,3/2;1) = 3 - ------ 2 (1/3) 3F2(1,2/3,1/6;4/3,1;1) = 2 (1/3) 2/3 (-18 + 9 2 ) 2 3F2(1,2/3,1/6;3/2,2;1) = - --------------------- 10 1/3 3 2 3F2(1,2/3,1/6;3/2,4/3;1) = 3 - ------ 2 2/3 3 2 3F2(1,2/3,1/6;3/2,1;1) = ------ 4 2/3 3 2 3F2(1,2/3,1/6;1,3/2;1) = ------ 4 (1/3) 3F2(1,2/3,1/6;1,4/3;1) = 2 2/3 2 3F2(1,2/3,1/6;1,1/2;1) = ---- 4 1/3 2 3F2(1,2/3,1/6;1,1/3;1) = ---- 3 1/3 4 2 3F2(1,2/3,1/2;5/6,7/3;1) = 2/5 + ------ 5 (1/3) 2/3 (-81 + 60 2 ) 2 3F2(1,5/6,1/3;8/3,2;1) = - ---------------------- 8 (1/3) 2/3 (36 - 33 2 ) 2 3F2(1,5/6,1/3;8/3,3/2;1) = - --------------------- 8 2/3 3 2 3F2(1,5/6,1/3;8/3,1;1) = ------ 4 (1/3) 2/3 (4 + 3 2 ) 2 3F2(1,5/6,1/3;8/3,1/2;1) = ------------------- 8 1/3 81 2 3F2(1,5/6,1/3;5/2,2;1) = - 27/2 + ------- 7 (1/3) 2/3 (81 - 72 2 ) 2 3F2(1,5/6,1/3;5/2,5/3;1) = - --------------------- 14 1/3 27 2 3F2(1,5/6,1/3;5/2,1;1) = ------- 28 (1/3) 2/3 (27 + 18 2 ) 2 3F2(1,5/6,1/3;5/2,2/3;1) = --------------------- 56 (1/3) 3F2(1,5/6,2/3;7/3,2;1) = -24 + 20 2 1/3 4 2 3F2(1,5/6,2/3;7/3,1;1) = ------ 3 (1/3) 2/3 (-28 + 21 2 ) 2 3F2(1,5/6,2/3;13/6,2;1) = - ---------------------- 2 2/3 7 2 3F2(1,5/6,2/3;13/6,1;1) = ------ 6 (1/3) 3F2(1,5/6,2/3;2,7/3;1) = -24 + 20 2 (1/3) 2/3 (-28 + 21 2 ) 2 3F2(1,5/6,2/3;2,13/6;1) = - ---------------------- 2 (1/3) 2/3 (-6 + 3 2 ) 2 3F2(1,5/6,2/3;2,7/6;1) = - -------------------- 2 (1/3) 3F2(1,5/6,2/3;2,4/3;1) = -6 + 6 2 (1/3) 2/3 (-9 + 6 2 ) 2 3F2(1,5/6,1/3;2,5/3;1) = - -------------------- 2 1/3 9 2 3F2(1,5/6,1/3;2,3/2;1) = - 9/2 + ------ 2 (1/3) 2/3 (3 - 6 2 ) 2 3F2(1,5/6,1/3;2,2/3;1) = - ------------------- 4 1/3 3 2 3F2(1,5/6,1/3;2,1/2;1) = 9/2 - ------ 2 (1/3) 3F2(1,5/6,2/3;4/3,2;1) = -6 + 6 2 (1/3) 3F2(1,5/6,2/3;4/3,1;1) = -2 2 1/3 9 2 3F2(1,5/6,1/3;3/2,2;1) = - 9/2 + ------ 2 (1/3) 2/3 (6 - 6 2 ) 2 3F2(1,5/6,1/3;3/2,5/3;1) = - ------------------- 2 1/3 3 2 3F2(1,5/6,1/3;3/2,1;1) = ------ 2 (1/3) 2/3 (-9 + 6 2 ) 2 3F2(1,5/6,1/3;5/3,2;1) = - -------------------- 2 (1/3) 2/3 (6 - 6 2 ) 2 3F2(1,5/6,1/3;5/3,3/2;1) = - ------------------- 2 (2/3) 3F2(1,5/6,1/3;5/3,1;1) = 2 (1/3) 2/3 (-6 + 3 2 ) 2 3F2(1,5/6,2/3;7/6,2;1) = - -------------------- 2 2/3 2 3F2(1,5/6,2/3;7/6,1;1) = - ---- 2 1/3 4 2 3F2(1,5/6,2/3;1,7/3;1) = ------ 3 2/3 7 2 3F2(1,5/6,2/3;1,13/6;1) = ------ 6 2/3 2 3F2(1,5/6,2/3;1,7/6;1) = - ---- 2 (1/3) 3F2(1,5/6,2/3;1,4/3;1) = -2 2 (2/3) 3F2(1,5/6,1/3;1,5/3;1) = 2 1/3 3 2 3F2(1,5/6,1/3;1,3/2;1) = ------ 2 2/3 2 3F2(1,5/6,1/3;1,2/3;1) = ---- 6 1/3 2 3F2(1,5/6,1/3;1,1/2;1) = ---- 4 (1/3) 3F2(1,1/3,1/6;2,11/6;1) = - 3/2 + 2 2 (1/3) 2/3 (-14 + 6 2 ) 2 3F2(1,1/3,1/6;2,5/3;1) = - --------------------- 10 (1/3) 2/3 (3 + 3 2 ) 2 3F2(1,1/3,1/6;2,2/3;1) = ------------------- 10 1/3 3 2 3F2(1,1/3,1/6;2,5/6;1) = 3/10 + ------ 5 (1/3) 3F2(1,1/3,1/6;11/6,2;1) = - 3/2 + 2 2 1/3 5 2 3F2(1,1/3,1/6;11/6,1;1) = ------ 6 (1/3) 2/3 (-14 + 6 2 ) 2 3F2(1,1/3,1/6;5/3,2;1) = - --------------------- 10 2/3 2 2 3F2(1,1/3,1/6;5/3,1;1) = ------ 3 1/3 3 2 3F2(1,1/3,1/6;5/6,2;1) = 3/10 + ------ 5 (1/3) 3F2(1,1/3,1/6;5/6,1;1) = 2 1/3 5 2 3F2(1,1/3,1/6;1,11/6;1) = ------ 6 2/3 2 2 3F2(1,1/3,1/6;1,5/3;1) = ------ 3 (2/3) 3F2(1,1/3,1/6;1,2/3;1) = 2 (1/3) 3F2(1,1/3,1/6;1,5/6;1) = 2 (1/3) 2/3 (3 + 3 2 ) 2 3F2(1,1/3,1/6;2/3,2;1) = ------------------- 10 (2/3) 3F2(1,1/3,1/6;2/3,1;1) = 2 > quit: memory used=31.4MB, alloc=76.3MB, time=0.25