`scipy.special._basic:riccati_yn`

source: /scipy/special/_basic.py :1333

Signature

def riccati_yn ( n , x )

Summary

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

Extended Summary

The Riccati-Bessel function of the second kind is defined here as $+ x y_{n} (x)$ , where $y_{n}$ is the spherical Bessel function of the second kind of order $n$ . Note that this is in contrast to a common convention that includes a minus sign in the definition.

This function computes the value and first derivative of the 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

yn : ndarray: Value of y0(x), ..., yn(x)
ynp : ndarray: First derivative y0'(x), ..., yn'(x)

Notes

The computation is carried out via ascending 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_yn