| Summary: | In 1979, Apéry proved the irrationality of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>. Since then, there has been much research interest in investigating the Apéry-like series for values of Riemann zeta function, Ramanujan-like series for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> 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.
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