scipy.special.itstruve0#

scipy.special.itstruve0(x, out=None) = <ufunc 'itstruve0'>#

Integral of the Struve function of order 0.

\[I = \int_0^x H_0(t)\,dt\]

Parameters:

xarray_like: Upper limit of integration (float).
outndarray, optional: Optional output array for the function values

Returns:

Iscalar or ndarray: The integral of \(H_0\) from 0 to x.

See also

struve: Function which is integrated by this function

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 itstruve0
>>> itstruve0(1.)
0.30109042670805547

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

>>> points = np.array([1., 2., 3.5])
>>> itstruve0(points)
array([0.30109043, 1.01870116, 1.96804581])

Plot the function from -20 to 20.

>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-20., 20., 1000)
>>> istruve0_values = itstruve0(x)
>>> fig, ax = plt.subplots()
>>> ax.plot(x, istruve0_values)
>>> ax.set_xlabel(r'$x$')
>>> ax.set_ylabel(r'$\int_0^{x}H_0(t)\,dt$')
>>> plt.show()

../../_images/scipy-special-itstruve0-1.png