Special functions and q-commuting variables

Abstract

This paper is mostly a survey, with a few new results. The first part deals with functional equations for q-exponentials, q-binomials and q-logarithms in q-commuting variables and more generally under q-Heisenberg relations. The second part discusses translation invariance of Jackson integrals, q-Fourier transforms and the braided line.Comment: plain TeX, 35 pages; Univ. of Amsterdam, Dept. of Math.; to appear in "Special Functions, q-Series and Related Topics", The Fields Institute Communications Series, minor revision, mainly linguisti