A First Order q-Difference System for the BC₁-Type Jackson Integral and Its Applications

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2009
• Main Author: Ito, M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149165
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A First Order q-Difference System for the BC₁-Type Jackson Integral and Its Applications / M. Ito // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 17 назв. — англ.

We present an explicit expression for the q-difference system, which the BC1-type Jackson integral (q-series) satisfies, as first order simultaneous q-difference equations with a concrete basis. As an application, we give a simple proof for the hypergeometric summation formula introduced by Gustafso...