New U?n+1?Extension Of WP-Bailey Lattice And New U?n+1?Bailey's_2?2Transformation Formula

Many different types of multivariate basic hypergeometric series generated from vari-ous group structures have formed numerous complex types of extension.These extensions have important application value in partial differential equation,multiple integral repre-sentation,combinatorial theory,algebraic expression theory and so on.The purpose of this paper is to study U(n+1)basic hypergeometric series associated with the unitary group.First,we introduce a new definition of U(n+1)WP-Bailey pair,and establish the chain structure of the U(n+1)WP-Bailey pairs.Then,uses iterative method to obtain a new U(n+1)transformation formula of basic hypergeometric series to give another new U(n+1)extensions of the three 10?9 transformation formulas.Finally,the new U(n+1)transformation formula,summation formula and its application of bilateral Bailey's 2?2 are obtained by using Cauchy method.Chapter 1 is about introduce some basic definitions and notations of basic hypergeo-metric series.Chapter 2 is about the definition of the new U(n+1)WP-Bailey pair,and creation of U(n+ 1)WP-Bailey chain and U(n+ 1)WP-Bailey latticeChapter 3 is about construction of a new transformation formula of U(n+1)basic hypergeometric series through iterative method and the derivation of another new U(n+1)10?9 transformation formula.Chapter 4 is about using the Cauchy method to obtain the new U(n+1)transformation formula and summation formula of the bilateral Bailey's 2?2.Multivariable generalizations of bilateral Rogers-Ramanujan identities and its some applications are given.