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.
Maximum order of function to compute
Argument at which to evaluate
Value of j0(x), …, jn(x)
First derivative j0’(x), …, jn’(x)
The computation is carried out via backward recurrence, using the relation DLMF 10.51.1 .
Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin .
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
NIST Digital Library of Mathematical Functions. https://dlmf.nist.gov/10.51.E1