
Appendix A
Basic Definitions of q-Calculus
Here we have collected some basic definitions and notions of q-calculus which are relevant to
the contents of the present book. As a reference, we would like to mention the book of Kac
and Cheung [622] and the recent book of Ernst [401], having a comprehensive bibliography
and also containing many historical remarks.
Let us assume that q ∈ C \{1}. Then the q-analog of a complex number z is defined by
[z]
q
=
1 − q
z
1 − q
. (A.1)
For a natural number n,oneobtains[n]
q
=1+q + q
2
+ ···q
n−1
with [0]
q
=1.Formost
of the arguments, one assumes that q is generic, that is, does not take a particular value.
However, when one conside ...