`scipy.special._mathieu:mathieu_cem`

source: build-install/usr/lib/python3.14/site-packages/scipy/special/_mathieu.py

Signature

def mathieu_cem(m, q, x, out = None)

Summary

Even Mathieu function and its derivative.

Extended Summary

Returns the even Mathieu function, ce_m(x, q), of order m and parameter q evaluated at x (given in degrees). Also returns the derivative with respect to x of ce_m(x, q)

Parameters

m : array_like: Order of the function
q : array_like: Parameter of the function
x : array_like: Argument of the function, given in degrees, not radians
out : tuple of ndarray, optional: Optional output arrays for the function results

Returns

y : scalar or ndarray: Value of the function
yp : scalar or ndarray: Value of the derivative vs x

Notes

The even Mathieu functions are the solutions to Mathieu's differential equation

\frac{d ^{2} y}{d x ^{2}} + (a_{m} - 2 q cos (2 x)) y = 0

for which the characteristic number $a_{m}$ (calculated with mathieu_a) results in an even, periodic solution $y (x)$ with period 180 degrees (for even $m$ ) or 360 degrees (for odd $m$ ).

Examples

Plot even Mathieu functions of orders ``2`` and ``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_cem(m, q, x)

✓

plt.plot(x, y)
plt.xlabel('x (degrees)')
plt.ylabel('y')
plt.legend(('m = 2', 'm = 4'))

✗

<matplotlib.legend.Legend object at 0x7f3f5917fe00>

Because the orders ``2`` and ``4`` are even, the period of each function is 180 degrees.

`scipy.special._mathieu:mathieu_cem`

Signature

Summary

Extended Summary

Parameters

Returns

Notes

Examples

See also

Aliases

Referenced by

This package