English

A symmetric formula for hypergeometric series

Combinatorics 2019-10-15 v2

Abstract

In terms of Dougall's 2H2_2H_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 Saalsch\"{u}tz's theorem. Similarly, we also show that Bailey's 6ψ6_6\psi_6 series identity implies the nonterminating form of Jackson's 8ϕ7_8\phi_7 summation formula. Considering the reversibility of the proofs, it is routine to show that Dougall's 2H2_2H_2 series identity is equivalent to a known nonterminating form of Saalsch\"{u}tz's theorem and Bailey's 6ψ6_6\psi_6 series identity is equivalent to the nonterminating form of Jackson's 8ϕ7_8\phi_7 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}
}
R2 v1 2026-06-23T01:32:56.489Z