# IJPAM: Volume 97, No. 2 (2014)

FACTORIZATIONS OF ANALYTIC FUNCTIONS VIA
GENERALIZED INVERSE POWER PRODUCT EXPANSIONS

H. Gingold, J. Quaintance
Department of Mathematics
West Virginia University
Morgantown WV 26506, USA
Department of Mathematics
Rutgers University-Hill Center for the Mathematical Sciences
Piscataway, NJ 08854-8019, USA

Abstract. Given an arbitrary sequence of complex numbers and an arbitrary nonzero sequence of complex numbers , we study the expansion of the Taylor series into infinite products of the form . Algebraic properties, convergence criteria, and combinatorial interpretations of the infinite products are investigated. We also provide an asymptotic formula for the majorizing product expansion associated with , .

AMS Subject Classification: 41A10, 30E10, 11P81, 05A17

Key Words and Phrases: power series, expansions, analytic functions, power products, generalized power products, generalized inverse power products, convergence, asymptotics, multi-sets, partitions, compositions

DOI: 10.12732/ijpam.v97i2.2 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 97
Issue: 2
Pages: 115 - 146
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