Summation formulae of special functions and multivariable Hermite polynomials

It is shown that summation formulae of special functions, often encountered in applications ranging from electromagnetic processes to combinatorics, can be written in terms of Hermite polynomials with more than one variable. The results are extended to generalized forms of Bessel functions, Hermite and Laguerre polynomials, including their multivariable extensions. It is shown that the ordinary Dobinsky identity and new generalizations as well can be derived as particular cases of the results obtained in this paper.