scipy.special.j1 — SciPy v1.15.2 Manual (original) (raw)

scipy.special.j1(x, out=None) = <ufunc 'j1'>#

Bessel function of the first kind of order 1.

Parameters:

xarray_like

Argument (float).

outndarray, optional

Optional output array for the function values

Returns:

Jscalar or ndarray

Value of the Bessel function of the first kind of order 1 at x.

See also

jv

Bessel function of the first kind

spherical_jn

spherical Bessel functions.

Notes

The domain is divided into the intervals [0, 8] and (8, infinity). In the first interval a 24 term Chebyshev expansion is used. In the second, the asymptotic trigonometric representation is employed using two rational functions of degree 5/5.

This function is a wrapper for the Cephes [1] routine j1. It should not be confused with the spherical Bessel functions (seespherical_jn).

References

Examples

Calculate the function at one point:

from scipy.special import j1 j1(1.) 0.44005058574493355

Calculate the function at several points:

import numpy as np j1(np.array([-2., 0., 4.])) array([-0.57672481, 0. , -0.06604333])

Plot the function from -20 to 20.

import matplotlib.pyplot as plt fig, ax = plt.subplots() x = np.linspace(-20., 20., 1000) y = j1(x) ax.plot(x, y) plt.show()