SciPy

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
nint

Maximum order of function to compute

xfloat

Argument at which to evaluate

Returns
jnndarray

Value of j0(x), …, jn(x)

jnpndarray

First derivative j0’(x), …, jn’(x)

Notes

The computation is carried out via backward recurrence, using the relation DLMF 10.51.1 [2].

Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin [1].

References

1

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

NIST Digital Library of Mathematical Functions. https://dlmf.nist.gov/10.51.E1

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