摘要
The unifiedΩ-series of the Gauss and Bailey2F1(1/2)-sums will be investigated by utilizing asymptotic methods and the modified Abel lemma on summation by parts.Several remarkable transformation theorems for theΩ-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 forπand the Catalan constant discovered by Guillera(2008).
作者
初文昌
Wenchang CHU(School of Mathematics and Statistics,Zhoukou Normal University,Zhoukou 466001,China;Department of Mathematics and Physics,University of Salento(P.O.Box 193),73100 Lecce,Italy)
