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arXiv · 0708.4354

G-functions and multisum versus holonomic sequences

Stavros Garoufalidis
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Abstract

The purpose of the paper is three-fold: (a) we prove that every sequence which is a multidimensional sum of a balanced hypergeometric term has an asymptotic expansion of Gevrey type-1 with rational exponents, (b) we construct a class of $G$-functions that come from enumerative combinatorics, and (c) we give a counterexample to a question of Zeilberger that asks whether holonomic sequences can be written as multisums of balanced hypergeometric terms. The proofs utilize the notion of a $G$-function, introduced by Siegel, and its analytic/arithmetic properties shown recently by André.

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Stavros Garoufalidis. 2008-11-12. G-functions and multisum versus holonomic sequences. https://arxiv.org/abs/0708.4354

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