scipy.special.it2i0k0#
- scipy.special.it2i0k0(x, out=None) = <ufunc 'it2i0k0'>#
Integrals related to modified Bessel functions of order 0.
Computes the integrals
\[\begin{split}\int_0^x \frac{I_0(t) - 1}{t} dt \\ \int_x^\infty \frac{K_0(t)}{t} dt.\end{split}\]- 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 it2i0k0 >>> int_i, int_k = it2i0k0(1.) >>> int_i, int_k (0.12897944249456852, 0.2085182909001295)
Evaluate the functions at several points.
>>> import numpy as np >>> points = np.array([0.5, 1.5, 3.]) >>> int_i, int_k = it2i0k0(points) >>> int_i, int_k (array([0.03149527, 0.30187149, 1.50012461]), array([0.66575102, 0.0823715 , 0.00823631]))
Plot the functions from 0 to 5.
>>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> x = np.linspace(0., 5., 1000) >>> int_i, int_k = it2i0k0(x) >>> ax.plot(x, int_i, label=r"$\int_0^x \frac{I_0(t)-1}{t}\,dt$") >>> ax.plot(x, int_k, label=r"$\int_x^{\infty} \frac{K_0(t)}{t}\,dt$") >>> ax.legend() >>> ax.set_ylim(0, 10) >>> plt.show()
