#### Abstract

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.

#### Disciplines

Applied Mathematics | Mathematics

#### Recommended Citation

He, Tian-Xiao; Hsu, Leetsch; and Shiue, Peter, "Multivariate Expansion Associated with Sheffer-type Polynomials and Operators" (2006). *Scholarship*. 16.

https://digitalcommons.iwu.edu/math_scholarship/16

## Comments

The

Bulletin of the Institute of Mathematics, Academia Sinicais published by the Institute of Mathematics, Academia Sinica, http://w3.math.sinica.edu.tw/bulletin/.