scipy.special.mathieu_odd_coef¶

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

Fourier coefficients for even Mathieu and modified Mathieu functions.

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

$\mathrm{se}_{2n+1}(z, q) = \sum_{k=0}^{\infty} B_{(2n+1)}^{(2k+1)} \sin (2k+1)z$
$\mathrm{se}_{2n+2}(z, q) = \sum_{k=0}^{\infty} B_{(2n+2)}^{(2k+2)} \sin (2k+2)z$

This function returns the coefficients $$B_{(2n+2)}^{(2k+2)}$$ for even input m=2n+2, and the coefficients $$B_{(2n+1)}^{(2k+1)}$$ 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. Bk : ndarray 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/f_src/special_functions/special_functions.html

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