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.
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)
The computation is carried out via backward recurrence, using the relation DLMF 10.51.1 [R571].
Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin [R570].
[R570] (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 [R571] (1, 2) NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/10.51.E1