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Super congruence for the Apéry numbers

Published online by Cambridge University Press:  22 January 2016

Tsuneo Ishikawa
Tsuneo Ishikawa*
Affiliation:
Department of Mathematics, Kobe University, Rokko, Kobe 657, Japan
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Let, for any n ≥ 0,

.

R. Apéry’s proof of the irrationality of ζ(2) and ζ(3) made use of these numbers (see [10]). As a result, many properties of the Apéry numbers were found (see [l]-[9]). In particular, Beukers and Stienstra showed the interesting congruence (see [11, Theorem 13.1]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 118 , June 1990 , pp. 195 - 202
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

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