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/f77_src/special_functions/special_functions.html [2]- NIST Digital Library of Mathematical Functions. https://dlmf.nist.gov/10.51.E1