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 - 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 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() 