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The Ramanujan Journal

, Volume 47, Issue 3, pp 501–508 | Cite as

Beukers-like supercongruences for generalized Apéry numbers

  • Gautam Kalita
Article
  • 118 Downloads

Abstract

For positive integers \(f_1,f_2,m,l\), the author and Chetry defined a generalization of Apéry numbers \(A(f_1,f_2,m,l,\lambda )\) given by
$$\begin{aligned} A(f_1,f_2,m,l,\lambda ):=\sum _{j=0}^{f_2}{f_1+j\atopwithdelims ()j}^m{f_2\atopwithdelims ()j}^l\lambda ^j. \end{aligned}$$
In this article, we prove certain Beukers-like supercongruences for these generalized Apéry numbers.

Keywords

Apéry numbers Gaussian hypergeometric series Supercongruences 

Mathematics Subject Classification

11A07 33C20 12E20 

Notes

Acknowledgements

We thank Ken Ono for going through the initial draft of the paper and many helpful suggestions. We are grateful to the referee for his/her helpful comments.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Sciences and MathematicsIndian Institute of Information Technology GuwahatiAssamIndia

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