hermite_product_display, a MATLAB code which displays an image of a function created by the Cartesian product of two Hermite polynomials, such as f(x,y) = h(3,x) * h(1,y).
There are five types of Hermite polynomial available. Perhaps the best behaved are "Hen(n,x)" and "Hf(n,x)", which don't blow up within the plotting interval as fast as the other functions do.
The physicist's Hermite polynomial H(n,x) can be defined by:
H(n,x) = (-1)^n exp(x^2/2) * d^n/dx^n ( exp(-x^2/2) )
The normalized physicist's Hermite polynomial Hn(n,x) is scaled so that
Integral ( -oo < X < +oo ) exp ( - X^2 ) * Hn(M,X) Hn(N,X) dX = delta ( N, M )
The probabilist's Hermite polynomial He(n,x) is related to H(n,x) by:
He(n,x) = H(n,x/sqrt(2)) / sqrt ( 2^n )
The normalized probabilist's Hermite polynomial Hen(n,x) is scaled so that
Integral ( -oo < X < +oo ) exp ( - 0.5*X^2 ) * Hen(M,X) Hen(N,X) dX = delta ( N, M )
The Hermite function Hf(n,x) is related to H(n,x) by:
Hf(n,x) = H(n,x) * exp(-x^2/2) / sqrt ( 2^n * n! * sqrt ( pi ) )
and is scaled so that:
Integral ( -oo < X < +oo ) Hf(M,X) Hf(N,X) dX = delta ( N, M )
hermite_product_display ( 'name', i, j )where
The computer code and data files described and made available on this web page are distributed under the MIT license
hermite_product_display is available in a MATLAB version.
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