Uniform convergence of hypergeometric series

2006/03/28 by Raimundas Vidunas, Vidunas, Raimundas
Mathematics · #33C20 #33F10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:33C20 #msc:33F10

paper · pdf · doi:10.48550/arxiv.math/0603646

42 pages, 2 Figures. A more compact form of hypergeometric terms is used. Examples added

arxiv created 2006/08/14 · arxiv updated 2009/12/01

Abstract

The considered problem is uniform convergence of sequences of hypergeometric series. We give necessary and sufficient conditions for uniformly dominated convergence of infinite sums of proper bivariate hypergeometric terms. These conditions can be checked algorithmically. Hence the results can be applied in Zeilberger type algorithms for nonterminating hypergeometric series.

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