# scipy.special.riccati_jn¶

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.

Parameters: 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)

Notes

The computation is carried out via backward recurrence, using the relation DLMF 10.51.1 [R505].

Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin [R504].

References

 [R504] (1, 2) Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. http://jin.ece.illinois.edu/specfunc.html
 [R505] (1, 2) NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/10.51.E1

#### Previous topic

scipy.special.spherical_kn

#### Next topic

scipy.special.riccati_yn