A Pair of Operator Summation Formulas and Their Applications

Tian-Xiao He, Leetsch C. Hsu, Dongsheng Yin

Research output: Journal ArticleArticlepeer-review


Two types of symbolic summation formulas are reformulated using an extension of Mullin–Rota’s substitution rule in [R. Mullin, G.-C. Rota, On the foundations of combinatorial theory: III. Theory of binomial enumeration, in: B. Harris (Ed.), Graph Theory and its Applications, Academic Press, New York, London, 1970, pp. 167–213], and several applications involving various special formulas and identities are presented as illustrative examples.

Original languageAmerican English
JournalComputers Mathematics with Applications
StatePublished - Oct 2009


  • Delta operator
  • Bernoulli number
  • Catalan number
  • Generalized harmonic number
  • Stirling numbers


  • Applied Mathematics
  • Mathematics

Cite this