Seven Hundreds of Exotic ₃F₂-Series Evaluated in π, √2 and log(1 + √2)

Abstract

By means of the linearization method, a nonterminating exotic ₃F₂-series with five free integer parameters is reduced to particular instances of a known Ω (x, y) function. With a help of the Kummer and Thomae transformations, ten large classes of ₃F₂-series are evaluated in terms of π, and log(1+). A collection of 700 elegant summation formulae is presented.