scipy.special.it2struve0#

scipy.special.it2struve0(x, out=None) = <ufunc 'it2struve0'>#

Integral related to the Struve function of order 0.

Returns the integral,

\[\int_x^\infty \frac{H_0(t)}{t}\,dt\]

where \(H_0\) is the Struve function of order 0.

Parameters:

xarray_like: Lower limit of integration.
outndarray, optional: Optional output array for the function values

Returns:

Iscalar or ndarray: The value of the integral.

See also

struve

Notes

Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin [1].

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

Examples

Evaluate the function at one point.

>>> import numpy as np
>>> from scipy.special import it2struve0
>>> it2struve0(1.)
0.9571973506383524

Evaluate the function at several points by supplying an array for x.

>>> points = np.array([1., 2., 3.5])
>>> it2struve0(points)
array([0.95719735, 0.46909296, 0.10366042])

Plot the function from -10 to 10.

>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-10., 10., 1000)
>>> it2struve0_values = it2struve0(x)
>>> fig, ax = plt.subplots()
>>> ax.plot(x, it2struve0_values)
>>> ax.set_xlabel(r'$x$')
>>> ax.set_ylabel(r'$\int_x^{\infty}\frac{H_0(t)}{t}\,dt$')
>>> plt.show()

../../_images/scipy-special-it2struve0-1.png