scipy.special.it2struve0#

scipy.special.it2struve0(x, out=None) = <wrapped_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].

Array API Standard Support

it2struve0 has support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	⛔
PyTorch	✅	⛔
JAX	✅	⛔
Dask	✅	n/a

For the NumPy backend, this function supports all NumPy ufunc keyword arguments. Other backends may support out, but typically none of the other ufunc kwargs. out is typically supported for CuPy and PyTorch, but not currently in cases where SciPy relies on a generic Array API implementation or, for PyTorch on CPU, falls back to the NumPy backend. out is never supported for JAX because JAX arrays are immutable. it2struve0 does not currently support out for the PyTorch backend.

See Support for the array API standard for more information.

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