scipy.special.riccati_jn¶

scipy.special.
riccati_jn
(n, x)[source]¶ Compute RicattiBessel function of the first kind and its derivative.
The RicattiBessel 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 RicattiBessel 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