Figure Properties - SERC

m m
Nn ( x)
= ( – 1)
legendre
m
Description P = legendre(n,X) computes the associated Legendre functions Pn ( x)
of
degree n and order m = 0,1,...,n, evaluated for each element of X. Argument
n must be a scalar integer, and X must contain real values in the domain
– 1 ≤ x ≤ 1 .
If X is a vector, then P is an (n+1)-by-q matrix, where q = length(X). Each
element P(m+1,i) corresponds to the associated Legendre function of degree n
and order m evaluated at X(i).
In general, the returned array P has one more dimension than X, and each
element P(m+1,i,j,k,...) contains the associated Legendre function of
degree n and order m evaluated at X(i,j,k,...). Note that the first row of P is
the Legendre polynomial evaluated at X, i.e., the case where m = 0.
S = legendre(n,X,'sch') computes the Schmidt seminormalized associated
m
Legendre functions Sn ( x)
.
N = legendre(n,X,'norm') computes the fully normalized associated
m
Legendre functions Nn ( x)
.
Examples Example 1. The statement legendre(2,0:0.1:0.2) returns the matrix
Example 2. Given,
X = rand(2,4,5);
n = 2;
P = legendre(n,X)
n 1 ⎛ + -- ⎞( n – m)!
⎝ 2⎠
m
---------------------------------------- P
( n + m)!
n ( x)
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
2-1299