Some Transformations for the Well-Poised \( _7F_6(1)\)​ -Series

Abstract

Several transformations about \(_\gamma F_6(1)\)-series are established by applying the modified Abel lemma on summation by parts. As a consequence, a reciprocal relation on balanced \(_3F_2(1)\)-series is derived, which may also be considered as a nonterminating extension of Saalschütz’s theorem (1891).