1 National Science Foundation (Youth grant 10801026) and basic research foundation (S8111116001) of Nanjing University of In- formation Science and Technology (Nanjing, China).
Several transformations about -series are established by applying the modified Abel lemma on summation by parts. As a consequence, a reciprocal relation on balanced -series is derived, which may also be considered as a nonterminating extension of Saalschütz’s theorem (1891).
