Research On Derived WP-Bailey Pairs,Rogers-Ramanujan Type Identities And Mock Theta Functions

In this paper,on the basis of Bailey and Andrews's works,we first utilize definitions of WP-Bailey pair and conjugate WP-Bailey pair to construct two derived WP-Bailey pairs of gen-eralized Lambert series identities.Secondly,we consider a several of Rogers-Ramanujan type identities by using q-Kummer₂?₁theorem and Carlitz inversion formula.Finally,we obtain two new representations of the fifth-order mock theta functions of bilateral series by the trans-formation lemma of Andrews,then we construct two third-order bilateral mock theta function identities,and we obtain fifth-order mock theta functions of the bilateral series of the radial limit.The main contents are as follows:In Chapter 1,we mainly introduce the historical background and development process of q-series theory,and then give the basic concepts,symbolic representations and some commonly used basic formulas of the problem to be studied in this paper.In Chapter 2,by using definitions of WP-Bailey pair and conjugate WP-Bailey pair,we obtain two new transformation formulas about the derived WP-Bailey pairs.As applications,through two₁₀?₉summation formulas,we get some identities about the derived WP-Bailey pair generalized Lambert series.In Chapter 3,on the basis of Carlitz's inversion works,by considering different inversion relations f(n)and g(n),we utilize Carlitz inversion formula and q-Kummer theorem to obtain a kind of new Rogers-Ramanujan type identities.In Chapter 4,based on the work of Andrews's transformation lemma,firstly,we choose different a_mand b_mfor the transformation lemma to obtain new representations of the fifth-order bilateral series mock theta function f₀(q)and f₁(q).Secondly,we obtain two bilateral third-order mock theta function(?)₀,(?)₁,(?)₀and(?)₁.Finally,the radial limit of the fifth-order bilateral mock theta function f₀(q),f₁(q),?₀(q)and?₁(q)obtained.