A symmetric formula for hypergeometric series

Chuanan Wei

paper

A symmetric formula for hypergeometric series

arXiv:1804.08612

Abstract

In terms of Dougall's $_{2} H_{2}$ 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 Saalschütz's theorem. Similarly, we also show that Bailey's $_{6} ψ_{6}$ series identity implies the nonterminating form of Jackson's $_{8} ϕ_{7}$ summation formula. Considering the reversibility of the proofs, it is routine to show that Dougall's $_{2} H_{2}$ series identity is equivalent to a known nonterminating form of Saalschütz's theorem and Bailey's $_{6} ψ_{6}$ series identity is equivalent to the nonterminating form of Jackson's $_{8} ϕ_{7}$ summation formula.