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Orthogonal Polynomials >> Orthogonal Polynomials > Hermite > hermite_norm

hermite_norm

Compute Hermite L2 norm

Calling Sequence

y=hermite_norm(n)

Parameters

n :

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

y :

a matrix of doubles, the norm

Description

Compute the integral

Examples

// Check that int Hn(x)^2 w(x) dx=sqrt(2pi) n!
// for w(x)=exp(-x^2/2)
function y=sqHew(x, n)
w=hermite_weight(x)
P=hermite_eval(x,n)
y=P^2*w
endfunction

for n = 1:5
[v,err]=intg(-10,10,list(sqHew,n));
disp([n,hermite_norm(n),v])
end

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