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Multivariate expansions associated with Sheffer-type polynomials and operators
by Tian Xiao He   Leetsch C. Hsu   Peter J.-S. Shiue

Vol. 1 No. 4 (2006) P.451~P.473

ABSTRACT

With the aid of multivariate She er-type polynomials and di erential 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 $A(\hat{t})f\widehat{(g(t))}$ (a composition of any given formal power series) and the expansion of the multivariate entire functions in terms of multivariate She er-type polynomials, which may be considered an application of the first expansion formula and the She er-type operators. The results are applicable to combinatorics and special function theory.

KEYWORDS
Multivariate formal power series, multivariate She er-type polynomials, multivariate She er-type di erential operators, multivariate weighted Stirling numbers, multivariate Riordan array pair, multivariate exponential polynomials

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 05A15, 11B73, 11B83, 13F25, 41A58

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