This is documentation for an old release of SciPy (version 0.19.0). Read this page in the documentation of the latest stable release (version 1.15.1).
scipy.special.spherical_jn¶
- scipy.special.spherical_jn(n, z, derivative=False)[source]¶
Spherical Bessel function of the first kind or its derivative.
Defined as [R524],
jn(z)=√π2zJn+1/2(z),where Jn is the Bessel function of the first 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: jn : ndarray
Notes
For real arguments greater than the order, the function is computed using the ascending recurrence [R525]. For small real or complex arguments, the definitional relation to the cylindrical Bessel function of the first kind is used.
The derivative is computed using the relations [R526],
j′n=jn−1−n+12jn.j′0=−j1New in version 0.18.0.
References
[R524] (1, 2) http://dlmf.nist.gov/10.47.E3 [R525] (1, 2) http://dlmf.nist.gov/10.51.E1 [R526] (1, 2) http://dlmf.nist.gov/10.51.E2