8 Sep
2015
8 Sep
'15
3:28 p.m.
Just a couple of days ago I wrote in a draft "Here are some other K transformations that are immediate specializations of hypergeometric transformations: EllipticK[z]==EllipticK[1/2 - (1/4)*Sqrt[-((z - 2)^2/(z - 1))]]/(1 - z)^(1/4) " Two misfortunes: This isn't quite right, and I lost its faulty derivation to a Mma front-end crash. The rather fishy plot of the error difference, Plot3D[Abs[Subtract @@ % /. z -> u + I*v], {u, 3/4, 9/4}, {v, -1, 1}, AxesLabel -> Automatic, PlotRange -> All] is gosper.org/marlin.png . I don't recall a prior case of two "analytic" functions agreeing everywhere but on a line segment. (In this case all the discrepancies have arg π/4.) --rwg