Abstract
The unified Ω-series of the Gauss and Bailey $$_2F_1(\frac{1}{2})$$-sums will be investigated by utilizing asymptotic methods and the modified Abel lemma on summation by parts. Several remarkable transformation theorems for the Ω-series will be proved whose particular cases turn out to be strange evaluations of nonterminating hypergeometric series and infinite series identities of Ramanujan-type, including a couple of beautiful expressions for π and the Catalan constant discovered by Guillera (2008).
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