Waldek Hebisch schrieb: > > did <firstname.lastname@example.org> wrote: > > > > Of course I expected a problem with > > branch cut. From my Byrd & Friedman > > I tried the (supposed) two equivalent definitions: > > > > N[JacobiAmplitude[1+I*2, 3/4], 20] > > 1.3306295147276587227 - 0.8831325397142208140 I > > > > N[ArcTan[JacobiCN[1+I*2, 3/4] , JacobiSN[1+I*2, 3/4]], 20] > > 1.8109631388621345158 + 0.8831325397142208140 I > > This definition is suboptimal, because it forces discontinuity > on real line. The definition I recall were continuous > (increasing) on real line.
And indeed that's what is shown in a Mathematica (I hope) graph
Beautiful! These six lines nail down a glaring Mathematica bug - a discrepancy in the numerical evaluation of nested functions. Some plots might help reveal if the problem is perhaps specific to nonzero Im[x] and/or m = 3/4: