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

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 AP Posts: 137 Registered: 3/4/09
Re: Product formula for Hermite polynomials
Posted: Jan 24, 2013 3:50 PM

On Sat, 19 Jan 2013 13:38:03 -0800 (PST), ksoileau
<kmsoileau@gmail.com> 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

http://thesis.library.caltech.edu/1861/1/wuan_thesis.pdf

lemme 2.2 with the proof

Date Subject Author
1/19/13 ksoileau
1/20/13 Don Redmond
1/20/13 ksoileau
1/20/13 Don Redmond
1/20/13 Roland Franzius
1/24/13 AP