TRIPLICATE DUAL SERIES OF THE 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 $-\frac{1}{27}$.