The Extension Of Bailey's Formula And Hecke-type Series Identities

Based on the Bailey's formula,we derive the generalized form of Bailey's formula by increasing the parameters.Then we study the Hecke-type series identities.We derive two q-series transformation formulae and some new Hecke-type series identities.The content is summarized as follows :In Chapter 1,we introduce the research background of basic hypergeometric series and Bailey's formula,explain briefly the basic concepts and some q-series formulae.Then we introduce the status of Hecke-type series identities.In Chapter 2,we respectively introduce the q-series formulae given by Liu and Andrews.In addition,we introduce some Hecke-type series identities obtained according to their formulae.In Chapter 3,based on the Bailey's formula,we derive the generalized form of Bailey's formula by increasing the parameters and rearranging series.We derive twoq-series transformation formulae by means of specializing the parameters appeared in the generalized formula and combinating the Liu's formula.Then we get some Hecke-type series identities.In Chapter 4,we summarize the thesis.