E.g.f. for Hermite

[Ralf Stephan]

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