scipy.special.lpmn

scipy.special.lpmn(m, n, z)

Associated Legendre functions of the first kind, Pmn(z) and its derivative, Pmn’(z) of order m and degree n. 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.

z can be complex.

Parameters :

m : int

|m| <= n; the order of the Legendre function

n : int

where n >= 0; the degree of the Legendre function. Often called l (lower case L) in descriptions of the associated Legendre function

z : float or complex

input value

Returns :

Pmn_z : (m+1, n+1) array

Values for all orders 0..m and degrees 0..n

Pmn_d_z : (m+1, n+1) array

Derivatives for all orders 0..m and degrees 0..n