
From:  Phyks 
Subject:  [Helpgsl] Different value for mathieu_ce in Mathematica and GSL 
Date:  Fri, 17 Feb 2017 16:53:27 +0100 
Useragent:  Roundcube Webmail/1.2.3 
Hi,I have some code that I prototyped in Mathematica and am now writing in C using GSL, that makes use of Mathieu functions. I have different results between the two of them, and I cannot figure out whether this is a bug in GSL, Mathematica or simply some misunderstanding from my part.
I am using `MathieuC` function in latest Mathematica (http://reference.wolfram.com/language/ref/MathieuC.html) which should be the same function as `gsl_sf_mathieu_ce` (https://www.gnu.org/software/gsl/manual/html_node/AngularMathieuFunctions.html#AngularMathieuFunctions) except that the former one takes a single `a` argument being the characteristic value whereas the GSL 2.3 implementation takes the order `n` and the `q` parameter directly.
So, I guess, ```
N[MathieuC[MathieuCharacteristicA[0, 1], 1, 2*Pi/180]]
1.41071 ``` should be equivalent to ``` gsl_sf_mathieu_ce(0, 1.0, 2.0 * M_PI / 180.0) ``` which gives a totally different value: 0.99751942347886335.I tried to debug with different values, and the discrepancies between Mathematica and GSL seems to appear only when the `q` parameter (1.0 here) is negative. If I take 1.0 instead, I get values in agreement. I tried to find yet another implementation to debug it, and found Scipy (https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.mathieu_cem.html#scipy.special.mathieu_cem) which relies on Fortran SPECFUN library apparently, and is in agreement with GSL.
I am missing something? Thanks!  Phyks
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