scipy.special.riccati_jn¶
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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: - n : int
Maximum order of function to compute
- x : float
Argument at which to evaluate
Returns: - jn : ndarray
Value of j0(x), …, jn(x)
- jnp : ndarray
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] (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. https://dlmf.nist.gov/10.51.E1