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MathGroup Archive 2007

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Fwd: Mathematica 6.0 bug in computing MathieuC

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80411] Fwd: [mg80300] Mathematica 6.0 bug in computing MathieuC
  • From: "taoufik bakri" <t.bakri at gmail.com>
  • Date: Tue, 21 Aug 2007 05:11:29 -0400 (EDT)
  • References: <200708170544.BAA00089@smc.vnet.net>

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
6.0does this all worng. You can check it yourself.

Regards,
T. Bakri

On 8/17/07, Curtis Osterhoudt <cfo at lanl.gov> wrote:
>
> On Thursday 16 August 2007 23:44:27 taoufik bakri 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. I
> noticed
> > that people already (October 2006) reported similar problems  with
> version
> > 5.2, yet version 6.0 still contains this bug!. Another CAS however
> computes
> > correctly both MathieuS and MathieuC.
> > Regards,
> > T. Bakri
>
> It might help if you gave an example of the error(s). I see nothing in the
> documentation about MathieuC being pi-periodic (except for special values
> of
> its parameters), nor do various plots of the function lend support to this
>
> assertion. Where's the bug?
>
> --
> ==========================================================
> Curtis Osterhoudt
> cfo at remove_this.lanl.and_this.gov
> PGP Key ID: 0x4DCA2A10
> Please avoid sending me Word or PowerPoint attachments
> See http://www.gnu.org/philosophy/no-word-attachments.html
> ==========================================================
>



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