lpmn(m, n, 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.
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.
|m| <= n
; the order of the Legendre function.
where n >= 0
; the degree of the Legendre function. Often called l
(lower case L) in descriptions of the associated Legendre function
Input value.
Values for all orders 0..m and degrees 0..n
Derivatives for all orders 0..m and degrees 0..n
Sequence of associated Legendre functions of the first kind.
clpmn
associated Legendre functions of the first kind for complex z
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.special._basic.clpmn
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