Some Hecke Type Identities And Mock Theta Functions

In this paper,on the basis of Liu’s work,we first use Bailey pair and Bailey inversion to construct two new q-series expansion formulae.Indeed,certain Hecke type identities involving theta functions and partial theta functions are discussed.Secondly,we consider Hecke type identities associated with classical mock theta functions by using the constant method.And two identities due to Liu can be proved by using the method.Finally,we obtain a finite form and further generalization of the identity of BsP-polynomial given by Andrews.In Chapter 1,we mainly review the development history of q-series,and introduce the historical background,basic definitions and some notations of our research projectIn Chapter 2,by employing Bailey pairs and Bailey inversion,we obtain two q-series expansion formulae.Indeed,some Hecke type identities can be obtained.In particular.we show that certain partial theta functions and the theta functions can be expressed in terms of Hecke type identitiesIn Chapter 3,on the basis of Andrews’s and Srivastava’s work,we show that certain mock theta functions can be expressed as constant terms in the Laurent series expansion of rational functions of theta functions.And,two identities given by Liu can be proved by using the constant term methodIn Chapter 4,we obtain a finite form and further generalization as well as applications of the identity of BsP-polynomial given by Andrews.