Associated Legendre function of the first kind, Pmn(z)
Computes the associated Legendre function of the first kind of order m and degree n,:
Pmn(z) = P_n^m(z)
and its derivative, Pmn'(z). Returns two arrays of size (m+1, n+1) containing Pmn(z) and Pmn'(z) for all orders from 0..m and degrees from 0..n.
This function takes a real argument z. For complex arguments z use clpmn instead.
Parameters: | m : int
n : int
z : float
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Returns: | Pmn_z : (m+1, n+1) array
Pmn_d_z : (m+1, n+1) array
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See also
Notes
In the interval (-1, 1), Ferrer’s function of the first kind is returned. The phase convention used for the intervals (1, inf) and (-inf, -1) is such that the result is always real.
References
[R210] | NIST Digital Library of Mathematical Functions http://dlmf.nist.gov/14.3 |