Abel's Lemma On Summation By Parts And Cubic Q-series Identities

By means of the Abel lemma on summation by parts,this thesis investigates a cubic basic hypergeometric series and its multi-parameter generalization.Some new cubic basic hypergeometric series transformation formulae are established,which generalize several known results.In Chapter 1,the author not only briefly reviews the related concepts,development and research status of basic hypergeometric series,but also describes the applications of Abel's lemma on summation by parts in basic hypergeometric series in detail.This lemma is the main research tool of this thesis.In Chapter 2,the Abel lemma on summation by parts is employed to investigate a nonterminating cubic basic hypergeometric series with 3-free parameters,and a new transformation formula for this series is obtained which can be seen as a q-analogy of a known 7F6-series summation formula due to Wang et al.(2018).In Chapter 3,the Abel lemma on summation by parts is applied to treat the partial sum of a cubic q-series with 4-free parameters which extends the cubic q-series in the last chapter.Two new transformations for this partial sum are established which generalize several terminating and nonterminating q-series summation and transformation formulae.In Chapter 4,the main results of this thesis are summarized and the future research work is prospected.