Bailey Pairs, U(n+1) Bailey Pairs And Their Applications

In this paper, we derive some q-series summation and transformation formulae in-cluding a 504 summation formula by using "simple" Bailey pairs. Then, we construct more summation and transformation formulae by the 5?4 summation formula and Bailey pairs. At last, we give some U(n+1) extensions of some summation and transformation formulae using U(n+1) Bailey pairs.In Chapter 1, we mainly introduce the history of q-series, basic definitions and some main notations.In Chapter 2. we use; "simple" Bailey pairs and Bailey's transform to obtain some summation and transformation formulae including a 5?4 summation formula.In Chapter 3, we derive a WP-Bailey pair, a WP-conjugate Bailey pair and a Bailey chain from the 5?4 summation formula. As applications, we obtain more summation and transformation formulae.In Chapter 4. we construct a U(n+1) extension of the Bailey chain above by using a U(n+1) generalization of the terminating balanced 3?2 summation theorem and give some applications.