The Application Of WP-bailey Lattice?multivariable Generalization And Elliptic Analogue

In this paper, we construct a new WP-Bailey lattice, and research basic hypergeomet-ric series of U(n + 1) WP-Bailey lattice and elliptic WP-Bailey lattice. We also derive a number of new transformations for multiple basic hypergeometric series.In Chapter 1, we mainly introduce the history of basic hypergeometric series, basic definitions and some main notations.In Chapter 2, we obtain the new WP-Bailey lattice and some applications by using the similar method of Agarwal-Andrews-Bressoud Bailey lattice.In Chapter 3, we get some applications of U(n+1) WP-Bailey lattice by the definition of U(n+ 1) WP-Bailey pair.In Chapter 4, we establish the new elliptic WP-Bailey lattice and give some applica-tions.