scipy.special.riccati_yn(n, x)[source]

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

The Ricatti-Bessel function of the second kind is defined as \(x y_n(x)\), where \(y_n\) is the spherical Bessel function of the second kind of order \(n\).

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


n : int

Maximum order of function to compute

x : float

Argument at which to evaluate


yn : ndarray

Value of y0(x), ..., yn(x)

ynp : ndarray

First derivative y0’(x), ..., yn’(x)


The computation is carried out via ascending recurrence, using the relation DLMF 10.51.1 [R478].

Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin [R477].


[R477](1, 2) Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996.
[R478](1, 2) NIST Digital Library of Mathematical Functions.