π-Formulae from Dual Series of the Dougall Theorem

2021/03/14 by Chu, Wenchang
#05A10 #11Y60 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2103.07872

Abstract

By means of the extended Gould-Hsu inverse series relations, we find that the dual relation of Dougall's summation theorem for the well--poised ₇F₆-series can be utilized to construct numerous interesting Ramanujan--like infinite series expressions for π^±1 and π^±2, including an elegant formula of π^-2 due to Guillera.

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