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

Authors:
Tian-Xiao He;Leetsch C. Hsu;Peter J. -S. Shiue
Affiliations:
Department of Mathematics and Computer Science, Illinois Wesleyan University, Bloomington, IL 61702-2900, USA;Department of Mathematics, Dalian University of Technology, Dalian 116024, PR China;Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154-4020, USA
Venue:
Computers & Mathematics with Applications
Year:
2007

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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.