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:
mint

Order of Mathieu functions. Must be non-negative.

qfloat (>=0)

Parameter of Mathieu functions. Must be non-negative.

Returns:
Akndarray

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

References

[1]

Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html

[2]

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