##
Lecture Notes For An Introductory Minicourse on
*q*-Series

**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.

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