A symmetric formula for hypergeometric series
Combinatorics
2019-10-15 v2
Abstract
In terms of Dougall's series identity and the series rearrangement method, we establish an interesting symmetric formula for hypergeometric series. Then it is utilized to derive a known nonterminating form of Saalsch\"{u}tz's theorem. Similarly, we also show that Bailey's series identity implies the nonterminating form of Jackson's summation formula. Considering the reversibility of the proofs, it is routine to show that Dougall's series identity is equivalent to a known nonterminating form of Saalsch\"{u}tz's theorem and Bailey's series identity is equivalent to the nonterminating form of Jackson's summation formula.
Keywords
Cite
@article{arxiv.1804.08612,
title = {A symmetric formula for hypergeometric series},
author = {Chuanan Wei},
journal= {arXiv preprint arXiv:1804.08612},
year = {2019}
}