scipy.special.lpmn¶
- scipy.special.lpmn(m, n, z)[source]¶
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.
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