G-函数与多和与完整序列
G-functions and multisum versus holonomic sequences
摘要：
本文件的目的有三个方面：（a）证明了平衡超几何项的多维和序列都有Gevrey型1有理指数渐近展开式，（b）构造了一类由计数组合学得到的$G$ -函数，（c）给出了Zeilberger问题的一个反例，该问题提出完整序列是否可以写成平衡超几何项的多重和.证明利用的概念$G$ -功能，介绍了西格尔，其分析/算术性质最近显示安德烈。
英文摘要：
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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