A symmetric formula for hypergeometric series

In terms of Dougall’s 2 H 2 series identity and the series rearrangement method, we establish a 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 nont...

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Bibliographic Details
Published in:The Ramanujan journal Vol. 55; no. 3; pp. 919 - 927
Main Author: Wei, Chuanan
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2021
Springer Nature B.V
Subjects:
Combinatorics
Equivalence
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Theorems
series identity
Hypergeometric series
Secondary 33C20
Dougall’s
Primary 05A19
Basic Hypergeometric series
Bailey’s
ISSN:1382-4090, 1572-9303
Online Access:Get full text
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Summary:In terms of Dougall’s 2 H 2 series identity and the series rearrangement method, we establish a 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.
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ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-019-00248-8