Samenvatting:
The fundamental idea of q-mathematics is simple: replace a
by (1-qa)/(1-q).
Applying this rule to special functions gives q-special functions, such as
q-gamma functions, q-exponential functions, q-Bessel functions etc.
Some of the pioneers in the field were Euler, Jacobi, Cauchy and Heine.
Their main motivation was applications in number theory.
In the last 15 years there has been an enormously increased interest in
q-mathematics, due to connections with quantum groups and infinite-dimensional
Lie-algebras.
In this talk I will give an elementary introduction to q-mathematics
and describe some applications to classical mathematics.