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Selected Works of Tian-Xiao He
Article
A Pair of Operator Summation Formulas and Their Applications
Computers & Mathematics with Applications (2009)
  • Tian-Xiao He, Illinois Wesleyan University
  • Leetsch C. Hsu, Dalian University of Technology
  • Dongsheng Yin
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Abstract

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.

Keywords
  • Delta operator,
  • Bernoulli number,
  • Catalan number,
  • Generalized harmonic number,
  • Stirling numbers
Disciplines
Publication Date
Fall October, 2009
Publisher Statement
Computers & Mathematics with Applications is published by Elsevier, http://www.journals.elsevier.com/computers-and-mathematics-with-applications/.
Citation Information
Tian-Xiao He, Leetsch C. Hsu and Dongsheng Yin. "A Pair of Operator Summation Formulas and Their Applications" Computers & Mathematics with Applications Vol. 58 Iss. 1 (2009)
Available at: http://works.bepress.com/tian_xiao_he/62/