Evaluations of series of the $q$-Watson, $q$-Dixon, and $q$-Whipple type

zbMATH Open1400.05032arXiv1307.4307MaRDI QIDQ4558963

Xiaoxia Wang, Chuanan Wei

Publication date: 30 November 2018

Abstract: Using $q$-series identities and series rearrangement, we establish several extensions of $q$-Watson formulas with two extra integer parameters. Then they and Sears' transformation formula are utilized to derive some generalizations of $q$-Dixon formulas and $q$-Whipple formulas with two extra integer parameters. As special cases of these results, many interesting evaluations of series of $q$-Watson,$q$-Dixon, and $q$-Whipple type are displayed.

Full work available at URL: https://arxiv.org/abs/1307.4307

zbMATH Keywords

\(q\)-Whipple formula\(q\)-Dixon formula\(q\)-Watson formula

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (2)

Summation formulae for \(q\)-Watson type \(4\phi 3\)-series ⋮ Analytical formulae for extended $_{3}F_{2}$-series of Watson–Whipple–Dixon with two extra integer parameters

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