scipy.special.lqmn

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

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

[R540]

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