scipy.special.j1#

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.

`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 (see `spherical_jn`).

References

[1]

Cephes Mathematical Functions Library, http://www.netlib.org/cephes/

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()
```