On Wed, Nov 21, 2012 at 8:54 PM, Bill Gosper <billgosper@gmail.com> wrote:
EllipticPi[1/3 (7 + 4 I √2), 1/81 (17 + 56 I √2)] == 1/9 (-7 + 4 I √2) EllipticPi[1/3 (7 - 4 I √2),1/81 (17 - 56 I √2)]
No responders. No surprise. Neil and I just spent several machine- hours finding exactly one other relation of the same shape: EllipticPi[1/2 (3+I √3),(3+I √3)/(3-I √3)]== (-1)^(5/6) EllipticPi[1/2 (3-I √3),(3-I √3)/(3+I √3)] We must have the shape wrong. --rwg
and EllipticPi[1/27 (7 + 4 I √2), 1/81 (17 + 56 I √2)] == 1/108 (81 I √2 EllipticK[1/9] - 27 I √2 EllipticK[1/81 (17 + 56 I √2)] + 27 (4 - I √2) EllipticPi[1/27 (7 - 4 I √2), 1/81 (17 - 56 I √2)] + (-64 + 25 I √2) EllipticPi[ 1/3 (7 - 4 I √2), 1/81 (17 - 56 I √2)]) ?--rwg