Processing math: 100%
SciPy

This is documentation for an old release of SciPy (version 0.18.0). Read this page in the documentation of the latest stable release (version 1.15.0).

scipy.special.mathieu_even_coef

scipy.special.mathieu_even_coef(m, q)[source]

Fourier coefficients for even Mathieu and modified Mathieu functions.

The Fourier series of the even solutions of the Mathieu differential equation are of the form

ce2n(z,q)=k=0A(2k)(2n)cos2kz
ce2n+1(z,q)=k=0A(2k+1)(2n+1)cos(2k+1)z

This function returns the coefficients A(2k)(2n) for even input m=2n, and the coefficients A(2k+1)(2n+1) for odd input m=2n+1.

Parameters:

m : int

Order of Mathieu functions. Must be non-negative.

q : float (>=0)

Parameter of Mathieu functions. Must be non-negative.

Returns:

Ak : ndarray

Even or odd Fourier coefficients, corresponding to even or odd m.

References

[R429]Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. http://jin.ece.illinois.edu/specfunc.html
[R430]NIST Digital Library of Mathematical Functions http://dlmf.nist.gov/28.4#i