A short proof for Gosper's F-7(6)-series conjecture

作者：Wang, Chenying^*; Chen, Xiaojing

来源：Journal of Mathematical Analysis and Applications, 2015, 422(2): 819-824.

DOI：10.1016/j.jmaa.2014.09.019

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

A new and elementary proof of a nonterminating cubic F-7(6)-series summation identity conjectured by Gosper in a letter to Askey is given by means of Abel's lemma on summation by parts. Meanwhile, an interesting nonterminating F-3(2)(3/4)-series summation formula, which is also listed in the letter of Gosper, is derived.

• 出版日期2015-2-15
• 单位南京信息工程大学; 中国石油大学（北京）