13 Nov
2018
13 Nov
'18
9:24 a.m.
Wow, that was quick—Eric fixed it already! Thanks Eric, and Boo-Hoo! I was really hoping there was a formula relating E to just K and K', and not K-dot nor E'. —rwg On Mon, Nov 12, 2018 at 11:24 PM Bill Gosper <billgosper@gmail.com> wrote:
http://mathworld.wolfram.com/CompleteEllipticIntegraloftheFirstKind.html Eqn (18) gives
Out[290]= K[Sqrt[1 - k^2]] == E[k]/(k (1 - k^2)) - K[k]/k (modulus convention) which translates to Mathematica (parameter convention) Out[284]= EllipticK[1 - k^2] == EllipticE[k^2]/(k (1 - k^2)) - EllipticK[k^2]/k which doesn't work. Could there be any such relation between K, K', and only one of {E, E'}, in light of Legendre's relation? —rwg