lpmn — SciPy v1.15.2 Manual (original) (raw)

scipy.special.

scipy.special.lpmn(m, n, z)[source]#

Sequence of associated Legendre functions of the first kind.

Computes the associated Legendre function of the first kind of order m and degree n, Pmn(z) = \(P_n^m(z)\), and its derivative, Pmn'(z). Returns two arrays of size (m+1, n+1) containing Pmn(z) andPmn'(z) for all orders from 0..m and degrees from 0..n.

This function takes a real argument z. For complex arguments zuse clpmn instead.

Deprecated since version 1.15.0: This function is deprecated and will be removed in SciPy 1.17.0. Please scipy.special.assoc_legendre_p_all instead.

Parameters:

mint

|m| <= n; the order of the Legendre function.

nint

where n >= 0; the degree of the Legendre function. Often called l (lower case L) in descriptions of the associated Legendre function

zarray_like

Input value.

Returns:

Pmn_z(m+1, n+1) array

Values for all orders 0..m and degrees 0..n

Pmn_d_z(m+1, n+1) array

Derivatives for all orders 0..m and degrees 0..n

See also

clpmn

associated Legendre functions of the first kind for complex z

Notes

In the interval (-1, 1), Ferrer’s function of the first kind is returned. The phase convention used for the intervals (1, inf) and (-inf, -1) is such that the result is always real.

References