Multiple Rogers-Ramanujan Type Identities And Mock Theta Functions

In this paper,on the basis of Lovejoy and Osburn's work,we first use a simple Bailey pair to construct five mock theta functions in the form of q-series double sums.And we establish the relations between these mock theta functions and classical ones.Secondly,we construct doubled mixed mock modular forms by using the constructed Bailey pair and the existing Bailey chains.Finally,we apply bilateral Bailey lemma and iterating method to establish new versions of multisum Rogers-Ramanujan identities.In Chapter 1,we mainly review the development history of basic hypergcomctric series,and introduce the historical background,basic definitions and some notations of our research project.In Chapter 2,by constructing a new Bailey pair to establish five new mock theta functions and derive identities between new mock theta functions and the classical ones.In Chapter 3,by using the constructed Bailey pair and Bailey chains established by Bressoud,Ismail and Stanton to obtain doubled mixed mock modular forms.In Chapter 4,by using bilateral Bailey lemma and iterating method to establish new versions of multisum Rogers-Ramanujan identities.