Summation And Transformation Formulae Of Bivariate Basic Hypergeometric Series

By combining series rearrangement with Sears transformation formulae, this thesis systematically investigates double hypcrgeometric series identities.The content is sum-marized as follows:1. By means of the transformations of Sears and Watson about the terminating balanced4φ3-series, we investigate the two terminating ijr-Kampe de Feriet series φ1:2;μ1:3;λ and φ2:1;μ2:2;λ. Several reduction and summation formulae arc established. They extend the corresponding known results about the double q-Clauscn scries.2. Three classes of semi-terminating g-Kampe de Feriet series are systematically inves-tigated via the transformations of Sears and Watson on the terminating balanced4φ3-scrics. Thirteen transformation theorems arc established, that arc utilized to derive several reduction and summation formulae for bivariate q-scrics.3. Nonterminating extensions of the Scars transformation arc established by combining series rearrangement with the q-Kummer-Thomae-Whipple transformation and the Hall transformation as well as two three-term transformation formulae of3φ2-series.