Uniform convergence of hypergeometric series

Details Uniform convergence of hypergeometric series Uniform convergence of hypergeometric series

2006-03-28

arxiv.org/abs/math/0603646v2

Mathematics

Classical Analysis and ODEs

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

Scientific paper

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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