Parameter Augmentation for Basic Hypergeometric Series, I

William Y. C. Chen and Zhi-Guo Liu

  Abstract:  This paper is motivated by the umbral calculus approach to ba- sic hypergeometric series as initiated by Goldman-Rota, Andrews, and Roman, et al. We develop a method of deriving hypergeo- metric identities by parameter augmentation, which means that a hypergeometric identity with multiple parameters may be derived from its special case obtained by reducing some parameters to zero. Many classical results on basic hypergeometric series easily fall into this framework.