Multivariate Expansion Associated with Sheffer-type Polynomials and Operators

Tian-Xiao He, Leetsch C. Hsu, Peter J.-S. Shiue

Research output: Journal ArticleArticlepeer-review


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.

Original languageAmerican English
JournalBulletin of the Institute of Mathematics, Academia Sinica
StatePublished - 2006


  • Multivariate formal power series
  • multivariate Sheffer-type polynomials
  • multivariate Sheffer-type differential operators
  • multivariate weighted Stirling numbers
  • multivariate Riordan array pair
  • multivariate exponential polynomials.


  • Applied Mathematics
  • Mathematics

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