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Module « scipy.special »

Fonction riccati_yn - module scipy.special

Signature de la fonction riccati_yn

def riccati_yn(n, x) 

Description

help(scipy.special.riccati_yn)

Compute Ricatti-Bessel function of the second kind and its derivative.

The Ricatti-Bessel function of the second kind is defined here as :math:`+x
y_n(x)`, where :math:`y_n` is the spherical Bessel function of the second
kind of order :math:`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
----------
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] 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

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