clpmn(m, n, z, type=3)
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
.
By default, i.e. for type=3
, phase conventions are chosen according to such that the function is analytic. The cut lies on the interval (-1, 1). Approaching the cut from above or below in general yields a phase factor with respect to Ferrer's function of the first kind (cf. lpmn
).
For type=2
a cut at |x| > 1
is chosen. Approaching the real values on the interval (-1, 1) in the complex plane yields Ferrer's function of the first kind.
|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.
takes values 2 or 3 2: cut on the real axis |x| > 1
3: cut on the real axis -1 < x < 1
(default)
Values for all orders 0..m
and degrees 0..n
Derivatives for all orders 0..m
and degrees 0..n
Associated Legendre function of the first kind for complex arguments.
lpmn
associated Legendre functions of the first kind for real z
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.special._basic.lpmn
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them