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) containing Qmn(z) and Qmn'(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 : complex
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
[R488] Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. http://jin.ece.illinois.edu/specfunc.html