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Orthogonal Polynomials >> Orthogonal Polynomials > Laguerre > laguerre_norm

laguerre_norm

Compute Laguerre L2 norm

Calling Sequence

y=laguerre_norm(n)

Parameters

n :

a 1-by-1 matrix of doubles, integer value, n>=0.

y :

a matrix of doubles, the norm

Description

Returns the integral:

where Ln is Laguerre polynomial and w is the Laguerre weight.

Examples

I=laguerre_norm(0) // Norm of L0
I=laguerre_norm(1) // Norm of L1
I=laguerre_norm(2) // Norm of L2

// Check that int Ln(x)^2 w(x) dx=1
// for w(x)=exp(-x)
function y=sqLw(x, n)
w=laguerre_weight(x)
Px=laguerre_eval(x,n)
y=Px^2*w
endfunction
for n = 1:5
[v,err]=intg(0,100,list(sqLw,n));
I=laguerre_norm(n);
mprintf("n=%d, I=%f, v=%f\n",n,I,v)
end

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