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Mathematics > Combinatorics

arXiv:1804.08612 (math)
[Submitted on 23 Apr 2018 (v1), last revised 12 Oct 2019 (this version, v2)]

Title:A symmetric formula for hypergeometric series

Authors:Chuanan Wei
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Abstract:In terms of Dougall's $_2H_2$ 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 Saalschütz's theorem. Similarly, we also show that Bailey's $_6\psi_6$ series identity implies the nonterminating form of Jackson's $_8\phi_7$ summation formula. Considering the reversibility of the proofs, it is routine to show that Dougall's $_2H_2$ series identity is equivalent to a known nonterminating form of Saalschütz's theorem and Bailey's $_6\psi_6$ series identity is equivalent to the nonterminating form of Jackson's $_8\phi_7$ summation formula.
Subjects: Combinatorics (math.CO)
Cite as: arXiv:1804.08612 [math.CO]
  (or arXiv:1804.08612v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1804.08612

Submission history

From: Chuanan Wei [view email]
[v1] Mon, 23 Apr 2018 00:39:04 UTC (9 KB)
[v2] Sat, 12 Oct 2019 14:13:37 UTC (10 KB)
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