Hermite Polynomials

We are to show that H'_n(x)=2nH_(n-1)(x)

I know this can be done by differentiating the generating function

exp[2xh-h^2]=SUM(0 to inf):H_n(x)*[h^n/n!]

Are there any other method available to prove it directly using the Hermite equation/DE for Hermite functions?

Quote:

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Originally Posted by kolahalb

We are to show that H'_n(x)=2nH_(n-1)(x)

I know this can be done by differentiating the generating function

exp[2xh-h^2]=SUM(0 to inf):H_n(x)*[h^n/n!]

Are there any other method available to prove it directly using the Hermite equation/DE for Hermite functions?

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Well, you can prove it directly from either the differential equation or from substitution of the solution to the differential equation into the recursion relation. But both methods are long and rather messy.

-Dan

OK,thank you.