MATLAB Functions

Associated Legendre functions

P = legendre(n,X)
S = legendre(n,X,'sch')

Definition

The Legendre functions are defined by:

where

is the Legendre polynomial of degree n:

The Schmidt seminormalized associated Legendre functions are related to the nonnormalized associated Legendre functions

by:

Description

P = legendre(n,X)

computes the associated Legendre functions of degree n and order m = 0,1,...,n, evaluated at X. Argument n must be a scalar integer less than 256, and X must contain real values in the domain

The returned array P has one more dimension than X, and each element P(m+1,d1,d2...) contains the associated Legendre function of degree n and order m evaluated at X(d1,d2...).

If X is a vector, then P is a matrix of the form:

S = legendre(...,'sch')

computes the Schmidt seminormalized associated Legendre functions

Examples

The statement legendre(2,0:0.1:0.2) returns the matrix:


	`x = 0`	`x = 0.1`	`x = 0.2`
m = 0	`0.5000`	`0.4850`	`0.4400`
m = 1	`0`	`0.2985`	`0.5879`
m = 2	`3.0000`	`2.9700`	`2.8800`

Note that this matrix is of the form shown at the bottom of the previous page.

Given,

X = rand(2,4,5); N = 2;
P = legendre(N,X)

Then size(P) is 3-by-2-by-4-by-5, and P(:,1,2,3) is the same as legendre(n,X(1,2,3)).

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