Lecture notes for an introductory minicourse on q-series

摘要

These lecture notes were written for a mini-course that was designed tointroduce students and researchers to {\it $q$-series,} which are also called{\it basic hypergeometric series} because of the parameter $q$ that is used asa base in series that are ``{\it over, above or beyond}'' the {\it geometricseries}. We start by considering $q$-extensions (also called $q$-analogues) ofthe binomial theorem, the exponential and gamma functions, and of the betafunction and beta integral, and then progress on to the derivations of rathergeneral summation, transformation, and expansion formulas, integralrepresentations, and applications. Our main emphasis is on methods that can beused to {\bf derive} formulas, rather than to just {\it verify} previouslyderived formulas.