5.7.2.14.3. 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

$$\mathrm{ce}_{2n}(z, q) = \sum_{k=0}^{\infty} A_{(2n)}^{(2k)} \cos 2kz$$

$$\mathrm{ce}_{2n+1}(z, q) = \sum_{k=0}^{\infty} A_{(2n+1)}^{(2k+1)} \cos (2k+1)z$$

This function returns the coefficients $A_{(2n)}^{(2k)}$ for even input m=2n, and the coefficients $A_{(2n+1)}^{(2k+1)}$ 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

[R339]

Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. http://jin.ece.illinois.edu/specfunc.html

[R340]

NIST Digital Library of Mathematical Functions http://dlmf.nist.gov/28.4#i