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...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	The Ramanujan journal Ročník 55; číslo 3; s. 919 - 927
Hlavní autor:	Wei, Chuanan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.08.2021 Springer Nature B.V
Témata:	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
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Popis
Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1382-4090 1572-9303
DOI:	10.1007/s11139-019-00248-8