scipy.special.mathieu_sem#
- scipy.special.mathieu_sem(m, q, x, out=None) = <ufunc 'mathieu_sem'>#
- Odd Mathieu function and its derivative - Returns the odd Mathieu function, se_m(x, q), of order m and parameter q evaluated at x (given in degrees). Also returns the derivative with respect to x of se_m(x, q). - Parameters:
- marray_like
- Order of the function 
- qarray_like
- Parameter of the function 
- xarray_like
- Argument of the function, given in degrees, not radians. 
- outtuple of ndarray, optional
- Optional output arrays for the function results 
 
- Returns:
- yscalar or ndarray
- Value of the function 
- ypscalar or ndarray
- Value of the derivative vs x 
 
 - See also - Notes - Odd Mathieu functions are the solutions to Mathieu’s differential equation \[\frac{d^2y}{dx^2} + (b_m - 2q \cos(2x))y = 0\]- for which the characteristic number \(b_m\) (calculated with - mathieu_b) results in an odd, periodic solution \(y(x)\) with period 180 degrees (for even \(m\)) or 360 degrees (for odd \(m\)).- References [1]- ‘Mathieu function’. Wikipedia. https://en.wikipedia.org/wiki/Mathieu_function - Examples - Plot odd Mathieu functions of orders - 2and- 4.- >>> import numpy as np >>> from scipy import special >>> import matplotlib.pyplot as plt >>> m = np.asarray([2, 4]) >>> q = 50 >>> x = np.linspace(-180, 180, 300)[:, np.newaxis] >>> y, _ = special.mathieu_sem(m, q, x) >>> plt.plot(x, y) >>> plt.xlabel('x (degrees)') >>> plt.ylabel('y') >>> plt.legend(('m = 2', 'm = 4')) - Because the orders - 2and- 4are even, the period of each function is 180 degrees.