riccati_jn — SciPy v1.15.2 Manual (original) (raw)

scipy.special.

scipy.special.riccati_jn(n, x)[source]#

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

The Ricatti-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 Ricatti-Bessel function for all orders up to and including n.

Parameters:

nint

Maximum order of function to compute

xfloat

Argument at which to evaluate

Returns:

jnndarray

Value of j0(x), …, jn(x)

jnpndarray

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].

References