A nonterminating F-7(6)-series evaluation

作者：Wang, Chenying^*; Dai, Jingjing; Mezo, Istvan

来源：Integral Transforms and Special Functions, 2018, 29(9): 719-724.

DOI：10.1080/10652469.2018.1492571

• Generalized hypergeometric series
• a new F-7(6)-sum
• F-3(2)(3/4)-sum
• Abel's lemma on summation by parts

A strange nonterminating F-7(6)-series formula was conjectured by Gosper and was confirmed subsequently by Gasper and Rahman, who evaluated another similar F-7(6)-sum. By means of the modified Abel lemma on summation by parts, we prove an analogous strange nonterminating F-7(6)-series summation formula, extending both a terminating F-7(6)-sum and a nonterminating 3F2(3/4)-series evaluated by Chu through inverse series relations and the modified Abel lemma on summation by parts.

• 出版日期2018
• 单位南京信息工程大学