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..mand 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/f77_src/special_functions/special_functions.html