riccati_yn#
- scipy.special.riccati_yn(n, x)[source]#
- Compute Ricatti-Bessel function of the second kind and its derivative. - The Ricatti-Bessel function of the second kind is defined here as \(+x y_n(x)\), where \(y_n\) is the spherical Bessel function of the second kind of order \(n\). Note that this is in contrast to a common convention that includes a minus sign in the definition. - This function computes the value and first derivative of the function for all orders up to and including n. - Parameters:
- nint
- Maximum order of function to compute 
- xfloat
- Argument at which to evaluate 
 
- Returns:
- ynndarray
- Value of y0(x), …, yn(x) 
- ynpndarray
- First derivative y0’(x), …, yn’(x) 
 
 - Notes - The computation is carried out via ascending 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