Triplicate Dual Series of Dougall--Dixon Theorem

Abstract

Applying the triplicate form of the extended Gould--Hsu inverse series relations to Dougall's summation theorem for the well--poised ${}_7{F}_6$-series, we establish, from the dual series, several interesting Ramanujan--like infinite series expressions for ${\pi }^2$ and ${\pi }^{\pm 1}$ with convergence rate "$-\frac{1}{27}$".