This is documentation for an old release of SciPy (version 0.18.1). Read this page in the documentation of the latest stable release (version 1.15.1).
scipy.special.spherical_yn¶
- scipy.special.spherical_yn(n, z, derivative=False)[source]¶
Spherical Bessel function of the second kind or its derivative.
Defined as [R469],
yn(z)=√π2zYn+1/2(z),where Yn is the Bessel function of the second kind.
Parameters: n : int, array_like
Order of the Bessel function (n >= 0).
z : complex or float, array_like
Argument of the Bessel function.
derivative : bool, optional
If True, the value of the derivative (rather than the function itself) is returned.
Returns: yn : ndarray
Notes
For real arguments, the function is computed using the ascending recurrence [R470]. For complex arguments, the definitional relation to the cylindrical Bessel function of the second kind is used.
The derivative is computed using the relations [R471],
y′n=yn−1−n+12yn.y′0=−y1New in version 0.18.0.
References
[R469] (1, 2) http://dlmf.nist.gov/10.47.E4 [R470] (1, 2) http://dlmf.nist.gov/10.51.E1 [R471] (1, 2) http://dlmf.nist.gov/10.51.E2