
Re: Product formula for Hermite polynomials
Posted:
Jan 20, 2013 6:38 PM


On Sunday, January 20, 2013 2:01:10 PM UTC6, ksoileau wrote: > On Saturday, January 19, 2013 3:38:03 PM UTC6, 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!
www.math.niu.edu/~rusin/knownmath/99/prodhermite
L. Carlitz, The product of certain polynomial analogues to the Hermite polynomials, Amer. Math. Monthly 64(1957), 723725
Hope these help.
Don

