scipy.special.riccati_yn¶

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.

Parameters:

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)

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 [R513].

Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin [R512].

References

[R512]

(1, 2) Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. http://jin.ece.illinois.edu/specfunc.html

[R513]

(1, 2) NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/10.51.E1