A nonterminating 7F6-series evaluation

ABSTRACT

A strange nonterminating ${}_7{F}_6$-series formula was conjectured by Gosper and was confirmed subsequently by Gasper and Rahman, who evaluated another similar ${}_7{F}_6$-sum. By means of the modified Abel lemma on summation by parts, we prove an analogous strange nonterminating ${}_7{F}_6$-series summation formula, extending both a terminating ${}_7{F}_6$-sum and a nonterminating ${}_3{F}_2\left(3/4\right)$-series evaluated by Chu through inverse series relations and the modified Abel lemma on summation by parts.

KEYWORDS:

• Generalized hypergeometric series
• a new ${}_7{F}_6$-sum
• ${}_3{F}_2\left(3/4\right)$-sum
• Abel's lemma on summation by parts

2000 AMS Subject Classifications:

• Primary: 33C20
• Secondary: 40G10

Acknowledgements

The authors are sincerely grateful to the anonymous referee for the careful reading and useful suggestions, which have improved the manuscript to the present version.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is partially supported, during this work, by the National Natural Science Foundation of China under Grant No. 11601239 and the Natural Science Foundation of Shandong Province under Grant No. ZR2017QA012.