Some Closed-Form Evaluations of Multiple Hypergeometric and q-Hypergeometric Series - Lin, Shy-Der; Srivastava, H. M. (Acta applicandae mathematicae, 2005)
The main object of the present paper is to show how some fairly general analytical tools and techniques can be applied with a view to deriving summation, transformation and reduction formulas for multiple hypergeometric and multiple basic (or q-) hypergeometric series. By making use of some reduction formulas for multivariable hypergeometric functions, the authors investigate several closed-form evaluations of various families of multiple hypergeometric and q-hypergeometric series. Relevant connections of the results presented in this paper with those obtained in earlier works are also considered. A number of multiple q-series identities, which are developed in this paper, are observed to be potentially useful in the related problems involving closed-form evaluations of multivariable q-hypergeometric functions. [PUBLICATION ABSTRACT]