The U(n+1) WP-Bailey Pairs And The U(n+1)WP-Bailey Chains

In this thesis, we mainly research the U(n+1) basic hypergeometric series, proposethe definition of U(n+1) WP-Bailey pair, obtain U(n+1) WP-Bailey transformationand U(n+1) WP-Bailey chains, and we also derive a number of new transformations formultiple basic hypergeometric series.In Chapter1, we mainly introduce basic definitions and some main notations in basichypergeometric series.In Chapter2, we propose the definition of U(n+1) WP-Bailey pair by examiningthe Bailey method for proving Bailey’s10φ9transformation, we also present some specialapplications.In Chapter3, motivated by James and Peter [1], we derive U(n+1) generalizationsof a number of general WP-Bailey chains, and we also obtain some applications of theU(n+1) WP-Bailey chains.In Chapter4, we get U(n+1) generalization of two general formulas and some newU(n+1) basic hypergeometric series.