On Several Results Associated with the Apéry-like Series

Document Type

Article

Publication Title

Symmetry

Abstract

In 1979, Apéry proved the irrationality of (Formula presented.) and (Formula presented.). Since then, there has been much research interest in investigating the Apéry-like series for values of Riemann zeta function, Ramanujan-like series for (Formula presented.) and other infinite series involving central binomial coefficients. The purpose of this work is to present the first 20 results related to the Apéry-like series in the form of 4 lemmas, each containing 5 results. The Sherman’s results are applied to attain this. Thereafter, these 20 results are further used to establish up to 104 results pertaining to the Apéry-like series in the form of 4 theorems, with 26 results each. These findings are finally been described in terms of the generalized hypergeometric functions. Symmetry occurs naturally in the generalized hypergeometric functions.

DOI

10.3390/sym15051022

Publication Date

5-1-2023

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