`scipy.special._basic:riccati_jn`

source: /scipy/special/_basic.py :1277

Signature

def riccati_jn ( n , x )

Summary

Compute Riccati-Bessel function of the first kind and its derivative.

Extended Summary

The Riccati-Bessel function of the first kind is defined as $x j_{n} (x)$ , where $j_{n}$ is the spherical Bessel function of the first kind of order $n$ .

This function computes the value and first derivative of the Riccati-Bessel function for all orders up to and including n.

Parameters

n : int: Maximum order of function to compute
x : float: Argument at which to evaluate

Returns

jn : ndarray: Value of j0(x), ..., jn(x)
jnp : ndarray: First derivative j0'(x), ..., jn'(x)

Notes

The computation is carried out via backward recurrence, using the relation DLMF 10.51.1 ^[2].

Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin ^[1].

Aliases

scipy.special.riccati_jn