Re: [Help-gsl] Different value for mathieu_ce in Mathematica and GSL

[Patrick Alken]

Hello,

  I'm not familiar with the mathieu functions, but I entered your 
report into the bug tracker so hopefully someone with more knowledge 
than I can take a look and fix it.

On 02/17/2017 08:53 AM, Phyks wrote:
> 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/Angular-Mathieu-Functions.html#Angular-Mathieu-Functions) 
> 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!