Triplicate Dual Series of Dougall--Dixon Theorem

TL;DR

This paper extends Dougall's $_7F_6$ summation theorem using triplicate dual series relations to derive new Ramanujan-like infinite series for powers of pi, with a specific convergence rate.

Contribution

It introduces a novel application of triplicate dual series relations to Dougall's theorem, resulting in new series expressions for pi.

Findings

Derived Ramanujan-like series for π, π^2, and π^{-1}

Established convergence rate of -1/27 for these series

Extended the theoretical framework of inverse series relations

Abstract

Applying the triplicate form of the extended Gould--Hsu inverse series relations to Dougall's summation theorem for the well--poised $_7F_6$-series, we establish, from the dual series, several interesting Ramanujan--like infinite series expressions for $\pi^2$ and $\pi^{\pm1}$ with convergence rate "$-\frac{1}{27}$".