A ring is said to satisfy the strong 2-sum property if every element is a sum of two commuting units.In this note,we present some sufficient or necessary conditions for the matrix ring over a commutative local ring to...A ring is said to satisfy the strong 2-sum property if every element is a sum of two commuting units.In this note,we present some sufficient or necessary conditions for the matrix ring over a commutative local ring to have the strong 2-sum property.展开更多
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-ser...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).展开更多
基金This research was supported by the Natural Science Foundation of China(grants 11661014,11661013,11961050)the Guangxi Natural Science Foundation(grant no.2016GXNSFDA380017)a Discovery Grant from NSERC of Canada(grant no.RGPIN-2016-04706).
文摘A ring is said to satisfy the strong 2-sum property if every element is a sum of two commuting units.In this note,we present some sufficient or necessary conditions for the matrix ring over a commutative local ring to have the strong 2-sum property.
基金Supported by National High Technology Research and Development Program of China (863 Program) (2006AA04Z183), National Natural Science Foundation of China (60621001, 60534010, 60572070, 60774048, 60728307), Program for Changjiang Scholars and Innovative Research Groups of China (60728307, 4031002)
文摘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).