Re: Mathematica 6.0 bug in computing MathieuC

*To*: mathgroup at smc.vnet.net*Subject*: [mg80403] Re: Mathematica 6.0 bug in computing MathieuC*From*: T.bakri at gmail.com*Date*: Tue, 21 Aug 2007 05:07:20 -0400 (EDT)*References*: <fabgsc$ien$1@smc.vnet.net>

On Aug 20, 9:46 am, chuck009 <dmili... at comcast.com> wrote: > > Dear all, > > Something is still worng with the algorithm behind > > computing MathieuC. It > > reprts, for instance that MathieuC is pi-periodic > > when its not. > > Hey T, I was unable to cause the following code to fail to give a pi-periodic function "poly" for any natural number r and parameter q: > > r = 4; > q = -3 - 3*I > a = N[MathieuCharacteristicA[r, q]] > poly = MathieuC[a, q, x]/Exp[I*r*x]; > p1 = Plot[Im[poly], {x, 0, 10}]; > linelist = (Line[{{#1*Pi, -3}, {#1*Pi, 3}}] & ) /@ Range[1, 3] > Show[{p1, Graphics[linelist]}] > > where the division by Exp[irx] is a consequence of Floquet's Theorem. Take the parameter c such that MathieuCharacteristicB[2, c]=1. One can easilty numerically compute c. We find c=-6.433074585014675206670244658478726486156264965498297244484. Clearly, we have MathieuS(1,c,t) is Pi-periodic. However MathieuC(1,c,t) should oscillate but is NOT Pi-periodic. Moreover the Wronski-determinant ( i.e. MathieuS(1,c,t)*MathieuCPrime(1,c,t) - MathieuC(1,c,t)*MathieuSPrime(1,c,t)) is in this case time-independent and must be equal to -1. Mathematica 6.0 does this all worng. You can check it yourself. Regards, T. Bakri