Inversion techniques and combinatorial identities: Balanced hypergeometric series

Abstract

Following the earlier works on Inversion techniques and combinatorial identities, the duplicate form of the Gould-Hsu [18] inversion theorem is constructed. As applications, several terminating balanced hypergeometric formulas are demonstrated, including those due to Andrews [3], which have been the primary stimulation to the present research. Encouraged by the recent work of Standon [23], we establish two higher hypergeometricev aluations with three additional parameters, which specialize further to over two hundred hypergeometriciden tities. © 2002 Rocky Mountain Mathematics Consortium.