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Topic: Product formula for Hermite polynomials
Replies: 5   Last Post: Jan 24, 2013 3:50 PM

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ksoileau

Posts: 85
From: Houston, TX
Registered: 3/9/08
Re: Product formula for Hermite polynomials
Posted: Jan 20, 2013 3:01 PM
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On Saturday, January 19, 2013 3:38:03 PM UTC-6, ksoileau wrote:
> I'm looking for a formula which expresses the product of two Hermite polynomials as a linear combination of Hermite polynomials, i.e. $a_{m,n,i}$ verifying
>
> $$
>
> H_m(x)H_n(x)=\sum \limits_{i=0}^{m+n} a_{m,n,i} H_i(x).
>
> $$
>
> for all nonegative $m,n$.
>
>
>
> If such a formula is known, I'd be most appreciative of a citation or link describing it.
>
>
>
> Thanks for any help!
>
>
>
> Kerry M. Soileau


I already did that and found no answer to my question at any of these links:

http://en.wikipedia.org/wiki/Orthogonal_polynomials
http://mathworld.wolfram.com/HermitePolynomial.html
http://en.wikipedia.org/wiki/Hermite_polynomials

If the answer was so easy to find using Google, why did you take the trouble to write a reply without providing a link? You have a rather eccentric concept of "helpfulness."

Thanks anyway!



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