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.


n : int

Maximum order of function to compute

x : float

Argument at which to evaluate


jn : ndarray

Value of j0(x), ..., jn(x)

jnp : ndarray

First derivative j0’(x), ..., jn’(x)


The computation is carried out via backward recurrence, using the relation DLMF 10.51.1 [R518].

Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin [R517].


[R517](1, 2) Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996.
[R518](1, 2) NIST Digital Library of Mathematical Functions.