Seven Hundreds of Exotic ₃F₂-Series Evaluated in π, √2 and log(1 + √2)

Authors

DOI:

https://doi.org/10.37256/cm.2420211066

Keywords:

hypergeometric series, nonterminating exotic ₃F₂-series, linearization method, Thomae transformation, Kummer transformation

Abstract

By means of the linearization method, a nonterminating exotic 3F2-series with five free integer parameters is reduced to particular instances of a known Ω (x, y) function. With a help of the Kummer and Thomae transformations, ten large classes of 3F2-series are evaluated in terms of π, CM10665.jpg and log(1+CM10666.jpg). A collection of 700 elegant summation formulae is presented.

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Published

2021-11-05

How to Cite

1.
Chu W. Seven Hundreds of Exotic ₃F₂-Series Evaluated in π, √2 and log(1 + √2). Contemp. Math. [Internet]. 2021 Nov. 5 [cited 2024 Jul. 14];2(4):327-98. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/1066