# The one-dimensional harmonic oscillator

1. Nov 5, 2004

### eys_physics

Dealing with the one-dimensional harmonic oscillator I'm trying to find a general formula for
$$\int_{-\infty}^{\infty} \xi^p H_n(\xi) H_k(\xi) d\xi$$
there $$H_n(\xi)$$ and $$H_k(\xi)$$ are hermite polynomials and p is an integer ( $$p\geq 0$$).
I can found the answer for p=0 and p=1 but I can't find the formula for a general p so I need some hint how to do it.

Last edited: Nov 5, 2004
2. Nov 5, 2004

### dextercioby

I can't give you any hint,just the result:
http://functions.wolfram.com/PDF/HermiteH.pdf

3. Nov 5, 2004

### dextercioby

I think it's much more that in Abramowitz-Stegun.

4. Nov 8, 2004

### eys_physics

Hey
Can you tell me that you mean with Aramowitz-Stegun?

5. Nov 8, 2004

### dextercioby

It's "Milton Abramowitz and Irene A.Segun:<<Handbook of Mathematical Functions>>,Dover Publications Inc.,NewYork".Any edition.Famous book among physicists.
A better book for the integrals part is obviously:

But it's much easier with the "functions.wolfram.com" website.
I think it's free...

6. Nov 9, 2004