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[工程科技]Special functions and q-commuting variables
Special functions and q-commuting variables
Tom H. Koornwinder
Department of Mathematics
University of Amsterdam
Plantage Muidergracht 24
1018 TV Amsterdam, The Netherlands
email thk@wins.uva.nl
6
9 Abstract: This paper is mostly a survey, with a few new results. The first part deals with func-
9 tional equations for q-exponentials, q-binomials and q-logarithms in q-commuting variables and
1
more generally under q-Heisenberg relations. The second part discusses translation invariance of
g Jackson integrals, q-Fourier transforms and the braided line.
u
A
Last modified: August 26, 1996
6
2
Note: Report No. 1, Institut Mittag-Leffler, Djursholm, Sweden, 1995/96; q-alg/9608008;
2 to appear in “Special Functions, q-Series and Related Topics”, The Fields Institute Communications
v Series.
8
0
0
8 1. Introduction
0
6 Identities for special functions often involve several variables, even if the special function itself
9 depends on only one variable. In general these variables are real or complex, so they commute with
/ each other. The theory of quantum groups has been quite successful in producing identities for
g
l q-special funcions, in particular addition formulas, see e.g. the survey in Koelink [21, Section 1] and
a
- further references given there. Although quantum groups themselves abound of non-commuting
q variables satisfying certain relations, one usually does not find back a similar type of variables in
:
v the
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