`scipy.special._basic:mathieu_even_coef`

source: /scipy/special/_basic.py :1582

Signature

def mathieu_even_coef ( m , q )

Summary

Fourier coefficients for even Mathieu and modified Mathieu functions.

Extended Summary

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

ce_{2 n} (z, q) = k = 0 \sum \infty A_{(2 n)}^{(2 k)} cos 2 k z

ce_{2 n + 1} (z, q) = k = 0 \sum \infty A_{(2 n + 1)}^{(2 k + 1)} cos (2 k + 1) z

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

Aliases

scipy.special.mathieu_even_coef