Author: by George Gasper
Abstract: These lecture notes were written for a mini-course that was designed to introduce students and researchers to q-series, which are also called basic hypergeometric series because of the parameter q that is used as a base in series that are ``over, above or beyond'' the geometric series. We start by considering q-extensions (also called q-analogues) of the binomial theorem, the exponential and gamma functions, and of the beta function and beta integral, and then progress on to the derivations of rather general summation, transformation, and expansion formulas, integral representations, and applications. Our main emphasis is on methods that can be used to derive formulas, rather than to just verify previously derived formulas.
Key words. basic hypergeometric series, q-series, q-integrals, summation, transformation and expansion formulas
1991 Mathematics Subject Classification. Primary 33D15, 33D20, 33D65; Secondary 33D05, 33D45, 33D60, 33D90.