Special functions and q-commuting variables
Tom H. Koornwinder
TL;DR
This paper surveys the theory of special functions related to q-commuting variables, exploring functional equations, q-analogs, and invariance properties of q-integrals and transforms, with some new results included.
Contribution
It provides a comprehensive overview of q-special functions and introduces new results on functional equations and invariance properties in q-commuting frameworks.
Findings
Derived functional equations for q-exponentials, q-binomials, and q-logarithms.
Established translation invariance of Jackson integrals and q-Fourier transforms.
Presented new results on q-Heisenberg relations and braided line invariance.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical functions and polynomials · Advanced Mathematical Identities · Analytic Number Theory Research