- #1

capandbells

- 96

- 0

## Homework Statement

The Hermite polynomials [tex]H_n(x)[/tex] may be defined by the generating function

[tex]e^{2hx-h^2} = \sum_{n=0}^{\infty}H_n(x)\frac{h^n}{n!}[/tex]

Evaluate

[tex]\int^{\infty}_{-\infty} e^{-x^2/2}H_n(x) dx[/tex]

(this should be from -infinity to infinity, but for some reason the latex won't work!)

## Homework Equations

Given.

## The Attempt at a Solution

I know that for odd [tex]n[/tex], this integral is 0, but I have no idea how to evaluate it. I know that the Hermite polynomials are orthogonal with respect to the given weight function, but I don't think I can use that for this integral (also, that's not in my book, I just found it on wikipedia). I'm assuming I need to use the generating function to derive my answer somehow, but I can't imagine how I would do that.

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