Abel's method on summation by parts and theta hypergeometric series
This paper deals with summation formulae of terminating theta hypergeometric series. The authors develop an iterating machinery for evaluating such series. By employing this technique they present most of the known theta hypergeometric series identities, but they also find several new transformation and summation formulae. The authors give a brief introduction to theta hypergeometric series, then they present the iterating machinery including a modified Abel lemma on summation by parts. By means of this lemma the authors review most of the known theta hypergeometric series identities and discover several new theta summation formulae.
Bailey's transformation on terminating very-well-poised \(_{10}{}_\phi{}_9{}\)-series
scientific article; zbMATH DE number 5321399
scientific article