a Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China b Department of Mathematics, Northeast University, Shenyang 110005, PR China
Abstract:
Abel's lemma on summation by parts is reformulated to investigate systematically terminating theta hypergeometric series. Most of the known identities are reviewed and several new transformation and summation formulae are established. The authors are convinced by the exhibited examples that the iterating machinery based on the modified Abel lemma is powerful and a natural choice for dealing with terminating theta hypergeometric series.
