Congruences for generalized Apéry numbers and Gaussian hypergeometric series

被引：7

作者：

Kalita G. ^{[1
]}

Chetry A.S. ^{[1
]}

机构：

[1] Department of Mathematics and Sciences, Indian Institute of Information Technology Guwahati, Ambari, GNB Road, Assam

来源：

Research in Number Theory | / 3卷 / 1期

关键词：

Apéry numbers; Gaussian hypergeometric series; Supercongruences;

D O I：

10.1007/s40993-016-0069-z

中图分类号：

学科分类号：

摘要：

For positive integers f1, f2, m, l, we define a generalization of Apéry numbers A(f1, f2, m, l, λ) given by A(f1,f2,m,l,λ):=∑j=0f2(f1+jj)m(f2j)lλj.In this article, we deduce congruence relations satisfied by these generalized Apéry numbers extending results of (Coster in Supercongruences, Ph.D. thesis, Universiteit Leiden, 1988). We find expressions of A(f1, f2, m, l, λ) in terms of Gaussian hypergeometric series and evaluate some new supercongruences similar to Beukers’ supercongruences. © 2017, The Author(s).

引用

共 26 条

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