On Friday, 5 April 2013 03:00:38 UTC+2, Waldek Hebisch wrote: > This definition is suboptimal, because it forces discontinuity > > on real line. The definition I recall were continuous > > (increasing) on real line.
OK, but maple defines a discontinuous function over the real line. Try plot(JacobiAM(x,sqrt(3/4)),x=-10..20); plot(arctan(JacobiSN(x,sqrt(3/4)),JacobiCN(x,sqrt(3/4)))-JacobiAM(x,sqrt(3/4)),x=-10..20);
MMA, on the other hand, gives a continuous increasing function.
Does it mean that maple implement the Jacobi Amplitude via the suboptimal formula?