Terminating ₃F₂(4)-series extended with three integer parameters

ABSTRACT

By means of the linearization method, a large class of terminating ${}_3{F}_2\left(4\right)$-series, perturbed by three extra integer parameters are evaluated. Thirty-five closed summation formulae are presented as examples.

KEYWORDS:

• Hypergeometric series
• Chu–Vandermonde formula
• Pfaff–Saalschütz theorem
• linearization method
• telescoping method
• finite differences

2000 AMS SUBJECT CLASSIFICATIONS:

• Primary: 33C20
• Secondary: 05A10

Acknowledgements

The authors would like to thank the anonymous referees for their careful reading of the manuscript and valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is supported, during this work, by the Natural Science Foundation of Shandong Province of China [grant No. ZR2017QA012] and the National Natural Science Foundation of China [Grant No. 11201484].