scipy.special.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 as \(x y_n(x)\), where \(y_n\) is the spherical Bessel function of the second kind of order \(n\).
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/f_src/special_functions/special_functions.html
- 2
NIST Digital Library of Mathematical Functions. https://dlmf.nist.gov/10.51.E1