WP-Bailey Lattice And Elliptic WP-Bailey Lattice

In this paper, on the basis of AAB Bailey lattice, we first construct a new WP-Bailey lattice and obtain its elliptic WP-Bailey lattice. Then we obtain another new WP-Bailey lattice and some applications by making use of Andrews's second classical WP-Bailey chain and the non-linear WP-Bailey chain of Zhang and Huang.In Chapter 1, we mainly introduce the historical background of basic hypergeometric series, basic definitions and some notations.In Chapter 2, by applying the method of establishing AAB Bailey lattice, we construct a new WP-Bailey lattice and give its some applications.In Chapter 3, we obtain another new WP-Bailey lattice and some applications by making use of Andrews's second classical WP-Bailey chain and the non-linear WP-Bailey chain of Zhang and Huang.In Chapter 4, we establish the elliptic WP-Bailey lattice of AAB Bailey lattice and give some applications.