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Multivariate Expansion Associated With Sheffer-Type Polynomials And Operators, Tian-Xiao He, Leetsch Hsu, Peter Shiue
Multivariate Expansion Associated With Sheffer-Type Polynomials And Operators, Tian-Xiao He, Leetsch Hsu, Peter Shiue
Tian-Xiao He
With the aid of multivariate Sheffer-type polynomials and differential operators, this paper provides two kinds of general expansion formulas, called respectively the first expansion formula and the second expansion formula, that yield a constructive solution to the problem of the expansion of A(ˆt)f([g(t)) (a composition of any given formal power series) and the expansion of the multivariate entire functions in terms of multivariate Sheffer-type polynomials, which may be considered an application of the first expansion formula and the Sheffer-type operators. The results are applicable to combinatorics and special function theory.