WP-Bailey Lattice And Multivariable Generalization

In this paper, we construct a new WP-Bailey lattice, and research basic hypergeo-metric series of U(n+1) WP-Bailey lattice and some applications. Then, we propose the definition of Cl WP-Bailey pair, and obtain some applications of Cl WP-Bailey lattice. We also derive a number of new transformations for multiple basic hypergeometric series.In Chapter1, we mainly introduce the history of basic hypergeometric series, basic definitions and some main notations.In Chapter2, we obtain some applications of WP-Bailey lattice by using the similar method of Agarwal-Andrews-Bressoud Bailey lattice.In Chapter3, we get some applications of U(n+1) WP-Bailey lattice by the definition of U(n+1) WP-Bailey pair.In Chapter4, we propose the definition of Cl WP-Bailey pair by using Cl terminating6φ5summation theorem, then we deduce some applications of Cl WP-Bailey lattice.