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
- mint
Order of Mathieu functions. Must be non-negative.
- qfloat (>=0)
Parameter of Mathieu functions. Must be non-negative.
- Returns
- Bkndarray
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