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Commutation Relations, Normal Ordering, and Stirling Numbers
book

Commutation Relations, Normal Ordering, and Stirling Numbers

by Toufik Mansour, Matthias Schork
September 2015
Intermediate to advanced content levelIntermediate to advanced
528 pages
19h 34m
English
Chapman and Hall/CRC
Content preview from Commutation Relations, Normal Ordering, and Stirling Numbers
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
n1
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 ...
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Publisher Resources

ISBN: 9781466579897