# 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: 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)

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].

References

 [1] (1, 2) Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. https://people.sc.fsu.edu/~jburkardt/f_src/special_functions/special_functions.html
 [2] (1, 2) NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/10.51.E1

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