Evaluations of series of the \(q\)-Watson, \(q\)-Dixon, and \(q\)-Whipple type

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.