The U(n+1) Extensions Of Bailey Lattices And Carlitz Inversion Chains For Basic Hypergeometric Series

In this paper, we study basic hypergeometric series of Bailey lattices and some Carlitzinversion chains. we also get thier U(n+1) extensions and some relative applications.In Chapter1, we introduce some basic definitions and necessary notations about basichypergeometric series theory.In Chapter2, we construct two new U(n+1) Bailey pairs by using U(n+1) Baileylemma of multiple basic hypergeometric series, which can form two U(n+1) Bailey lattices.Then we also get some relative applications.In Chapter3, based on the theory of Gould-Hsu inversion, we can establish three newU(n+1) Carlitz inversions as the generalization of U(n+1) Bailey transformations, andgive some correlative applications.