LEGENDRE Function

Evaluates the associated Legendre functions.

Usage

P = LEGENDRE(n, m, x)

Input Parameters

n—A non-negative integer.

m—A non-negative integer less than or equal to n.

x—An array of values in the range [–1, 1].

Returned Value

P—An array of the same dimensions as x, containing the associated Legendre function P_n,m, evaluated at each x(i).

Input Keywords

Norm—If set then P_n,m is normalized by the factor:

 

Discussion

The associated LEGENDRE function is a solution of the associated Legendre differential equation:

 

If the keyword Norm is set, then the functions are normalized so that:

 

The LEGENDRE function is based on the work of Adrien-Marie Legendre.

Example

See wave/lib/user/examples/legendre_ex.