Triplicate Dual Series of Dougall--Dixon Theorem

英文摘要：

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 $π^2$ and $π^{\pm1}$ with convergence rate "$-\frac{1}{27}$".