scipy.special.riccati_yn¶
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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: - n : int
Maximum order of function to compute
- x : float
Argument at which to evaluate
Returns: - yn : ndarray
Value of y0(x), …, yn(x)
- ynp : ndarray
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] (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 [2] (1, 2) NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/10.51.E1