scipy.special.itmodstruve0#

scipy.special.itmodstruve0(x, out=None) = <ufunc 'itmodstruve0'>#

Integral of the modified Struve function of order 0.

\[I = \int_0^x L_0(t)\,dt\]

Parameters:

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

Returns:

Iscalar or ndarray: The integral of \(L_0\) from 0 to x.

See also

modstruve: Modified 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 itmodstruve0
>>> itmodstruve0(1.)
0.3364726286440384

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

>>> points = np.array([1., 2., 3.5])
>>> itmodstruve0(points)
array([0.33647263, 1.588285  , 7.60382578])

Plot the function from -10 to 10.

>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-10., 10., 1000)
>>> itmodstruve0_values = itmodstruve0(x)
>>> fig, ax = plt.subplots()
>>> ax.plot(x, itmodstruve0_values)
>>> ax.set_xlabel(r'$x$')
>>> ax.set_ylabel(r'$\int_0^xL_0(t)\,dt$')
>>> plt.show()

../../_images/scipy-special-itmodstruve0-1.png