E.g.f. for Hermite

[Karol PENSON]

   Dear Ralf, Thanks for the information. In fact Francisco de Salinas 
gave me this reference, where this E.G.F. appears for the first time.
       All the best Karol 


On Sat, 17 Apr 2004, Ralf Stephan wrote:

> Date: Sat, 17 Apr 2004 09:10:48 +0200
> From: Ralf Stephan <ralf at ark.in-berlin.de>
> To: penson at lptl.jussieu.fr, Seqfan at ext.jussieu.fr
> Subject: Re: E.g.f. for Hermite
> 
> Francisco de Salinas: 
> > Karol PENSON wrote:
> > 
> > >Dear Seqfans,I have a question related to my investigations of some
> > >integer sequences:
> > >
> > >  Do you know, or do you know how to obtain in closed form the exponential
> > >generating function of the Hermite polynomials whose order is a multiple
> > >of three, i.e. I am looking for , im Maple notation:
> > >
> > >        sum(t^n*HermiteH(3*n,x)/n!,n=0..infinity)=  ????
> > >
> > 
> > Only in terms of the hypergeometric function 2F0 or the Kummer function U 
> > (and hence, of the Whittaker function W).
> > 
> > See: 'A triple lacunary generating function for Hermite polynomials' by Ira 
> > M. Gessel and Pallavi Jayawant, 4 Mar 2004 ( 
> > http://arxiv.org/abs/math.CO/0403086 ), from where the following exponential 
> 
> See also Theorem 4.5 (and other results) in Ira M. Gessel,
> Applications of the Classical Umbral Calculus,
> http://arxiv.org/math.CO/0108121
> 
> 
> 
> ralf
> 

-- 
_________________________________________________________________________
Karol A. PENSON
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