Symbolization of generating functions; an application of the Mullin–Rota theory of binomial enumeration

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

Research output: Journal ArticleArticlepeer-review

Abstract

We have found that there are more than a dozen classical generating functions that could be suitably symbolized to yield various symbolic sum formulas by employing the Mullin–Rota theory of binomial enumeration. Various special formulas and identities involving well-known number sequences or polynomial sequences are presented as illustrative examples. The convergence of the symbolic summations is discussed.

Original languageAmerican English
JournalComputers and Mathematics with Applications
Volume54
StatePublished - 2007

Keywords

  • Generating function
  • symbolic sum formula
  • binomial enumeration
  • shift-invariant operator
  • delta operator
  • Bell number
  • Genocchi number
  • Euler number
  • Euler polynomial
  • Eulerian fraction
  • Bernoulli number
  • Bernoulli polynomial

Disciplines

  • Applied Mathematics
  • Mathematics

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