scipy.special.lqmn¶

scipy.special.
lqmn
(m, n, z)[source]¶ Sequence of associated Legendre functions of the second kind.
Computes the associated Legendre function of the second kind of order m and degree n,
Qmn(z)
= \(Q_n^m(z)\), and its derivative,Qmn'(z)
. Returns two arrays of size(m+1, n+1)
containingQmn(z)
andQmn'(z)
for all orders from0..m
and degrees from0..n
. Parameters
 mint
m <= n
; the order of the Legendre function. nint
where
n >= 0
; the degree of the Legendre function. Often calledl
(lower case L) in descriptions of the associated Legendre function zcomplex
Input value.
 Returns
 Qmn_z(m+1, n+1) array
Values for all orders 0..m and degrees 0..n
 Qmn_d_z(m+1, n+1) array
Derivatives for all orders 0..m and degrees 0..n
References
 1
Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. https://people.sc.fsu.edu/~jburkardt/f_src/special_functions/special_functions.html