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. 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

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