Volume 17, Issue 4, December 2010, Pages 429 - 443
Noncommutative Hypergeometric and Basic Hypergeometric Equations
Authors
Alessandro Conflitti
Michael J. Schlosser
CMUC, Centre for Mathematics, University of Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal,conflitt@mat.uc.pt
Fakultät für Mathematik, Universität Wien Nordbergstraße 15, A-1090 Vienna, Austria,michael.schlosser@univie.ac.at
Received 23 May 2007, Accepted 16 March 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110000982How to use a DOI?
- Keywords
- Noncommutative hypergeometric series; hypergeometric differential equation
- Abstract
Recently, J. A. Tirao [Proc. Nat. Acad. Sci. 100(14) (2003) 8138–8141] considered a matrix-valued analogue of the 2F1 Gauß hypergeometric function and showed that it is the unique solution of a matrix-valued hypergeometric equation analytic at z = 0 with value I, the identity matrix, at z = 0. We give an independent proof of Tirao's result, extended to the more general setting of hypergeometric functions over an abstract unital Banach algebra. We provide a similar (but more complicated-looking) result for a second type of noncommutative 2F1 Gauß hypergeometric function. We further give q-analogues for both types of noncommutative hypergeometric equations.
- Copyright
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Alessandro Conflitti AU - Michael J. Schlosser PY - 2021 DA - 2021/01/07 TI - Noncommutative Hypergeometric and Basic Hypergeometric Equations JO - Journal of Nonlinear Mathematical Physics SP - 429 EP - 443 VL - 17 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110000982 DO - 10.1142/S1402925110000982 ID - Conflitti2021 ER -