The unified Ω-series of the Gauss and Bailey $_2F_1(\tfrac12)$-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).
Wenchang CHU
. INFINITE SERIES FORMULAE RELATED TO GAUSS AND BAILEY $_2F_1(\tfrac12)$-SUMS[J]. Acta mathematica scientia, Series B, 2020
, 40(2)
: 293
-315
.
DOI: 10.1007/s10473-020-0201-y
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