scipy.special.itj0y0#
- scipy.special.itj0y0(x, out=None) = <ufunc 'itj0y0'>#
Integrals of Bessel functions of the first kind of order 0.
Computes the integrals
\[\begin{split}\int_0^x J_0(t) dt \\ \int_0^x Y_0(t) dt.\end{split}\]For more on \(J_0\) and \(Y_0\) see
j0
andy0
.- Parameters:
- xarray_like
Values at which to evaluate the integrals.
- outtuple of ndarrays, optional
Optional output arrays for the function results.
- Returns:
References
[1]S. Zhang and J.M. Jin, “Computation of Special Functions”, Wiley 1996
Examples
Evaluate the functions at one point.
>>> from scipy.special import itj0y0 >>> int_j, int_y = itj0y0(1.) >>> int_j, int_y (0.9197304100897596, -0.637069376607422)
Evaluate the functions at several points.
>>> import numpy as np >>> points = np.array([0., 1.5, 3.]) >>> int_j, int_y = itj0y0(points) >>> int_j, int_y (array([0. , 1.24144951, 1.38756725]), array([ 0. , -0.51175903, 0.19765826]))
Plot the functions from 0 to 10.
>>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> x = np.linspace(0., 10., 1000) >>> int_j, int_y = itj0y0(x) >>> ax.plot(x, int_j, label=r"$\int_0^x J_0(t)\,dt$") >>> ax.plot(x, int_y, label=r"$\int_0^x Y_0(t)\,dt$") >>> ax.legend() >>> plt.show()