Laguerre's gf

[Mitch Harris]

> 
>     Does anyone know closed form  of the following generating function
>      for the ordinary Laguerre polynomials:
> 
>     G(M;T,x)= sum( t^n*LaguerreL(n,x)/((n!)^M), n=0..infinity), for 
> M=2,3...          ?


http://www.efunda.com/math/Laguerre/index.cfm
http://functions.wolfram.com/HypergeometricFunctions/LaguerreLGeneral/11/
http://www.math.sfu.ca/~cbm/aands/page_784.htm (22.9.15)

L_n(x) = [z^n] exp(z x/ (z-1) )/(1 - z)