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

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Don Redmond

Posts: 56
Registered: 5/5/11
Re: Product formula for Hermite polynomials
Posted: Jan 20, 2013 6:38 PM
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On Sunday, January 20, 2013 2:01:10 PM UTC-6, ksoileau wrote:
> On Saturday, January 19, 2013 3:38:03 PM UTC-6, ksoileau wrote:
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> > 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
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> > $$
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> > H_m(x)H_n(x)=\sum \limits_{i=0}^{m+n} a_{m,n,i} H_i(x).
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> > $$
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> > for all nonegative $m,n$.
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> > If such a formula is known, I'd be most appreciative of a citation or link describing it.
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> > Thanks for any help!
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> > Kerry M. Soileau
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> I already did that and found no answer to my question at any of these links:
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> http://en.wikipedia.org/wiki/Orthogonal_polynomials
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> http://mathworld.wolfram.com/HermitePolynomial.html
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> http://en.wikipedia.org/wiki/Hermite_polynomials
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> 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."
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> Thanks anyway!


www.math.niu.edu/~rusin/known-math/99/prod-hermite

L. Carlitz, The product of certain polynomial analogues to the Hermite polynomials, Amer. Math. Monthly 64(1957), 723-725

Hope these help.

Don



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