scipy.special.it2j0y0#
- scipy.special.it2j0y0(x, out=None) = <ufunc 'it2j0y0'>#
- Integrals related to Bessel functions of the first kind of order 0. - Computes the integrals \[\begin{split}\int_0^x \frac{1 - J_0(t)}{t} dt \\ \int_x^\infty \frac{Y_0(t)}{t} dt.\end{split}\]- For more on \(J_0\) and \(Y_0\) see - j0and- y0.- 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 it2j0y0 >>> int_j, int_y = it2j0y0(1.) >>> int_j, int_y (0.12116524699506871, 0.39527290169929336) - Evaluate the functions at several points. - >>> import numpy as np >>> points = np.array([0.5, 1.5, 3.]) >>> int_j, int_y = it2j0y0(points) >>> int_j, int_y (array([0.03100699, 0.26227724, 0.85614669]), array([ 0.26968854, 0.29769696, -0.02987272])) - 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 = it2j0y0(x) >>> ax.plot(x, int_j, label=r"$\int_0^x \frac{1-J_0(t)}{t}\,dt$") >>> ax.plot(x, int_y, label=r"$\int_x^{\infty} \frac{Y_0(t)}{t}\,dt$") >>> ax.legend() >>> ax.set_ylim(-2.5, 2.5) >>> plt.show() 