Elliptic Well-Poised Bailey Chains And Transformations Of Hypergeometric Series

This thesis is devoted to the problem of the elliptic well-poised Bailey chains as well as its applications to elliptic hypergeometric series, particular basic hypergeometric series. All those depend on the inverse technique.Chapter one serves as an introduction to the history of hypergeometric series and the inverse technique. Some notations, concepts, and results, as required for forthcoming discussion, are introduced.Chapter two is the main part of this paper. Therein, we put forward the problem of the characteristic equation of WP-Bailey chains and consequently give two kinds of solutions for the characteristic equation by the inverse technique . Some new results such as Bailey's Lemma for usual WP-Bailey pairs are established in the set of elliptic hypergeometric series.Chapter three contains many interesting results as the application of the last chapter. Among them is a new elliptic WP-Bailey chain, a WP-Bailey chain, and two ordinary Bailey chains. By making use of these chains, we establish some transformation formulas and summation formulas of hypergeometric series.In the last chapter, we consider an inverse relation originally due to Chu and Wang from the point view of elliptic hypergeometric series. Its elliptic analogue reveals a previously unknown dual relation between some known elliptic hypergeometric series summation formulas.