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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 041, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.041 (Mi sigma387) 		 
This article is cited in 6 scientific papers (total in 6 papers)

A First Order $q$-Difference System for the $BC_1$-Type Jackson Integral and Its Applications

Masahiko Ito

Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 229-8558, Japan
Full-text PDF (262 kB) Citations (6)
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DOI: https://doi.org/10.3842/SIGMA.2009.041
Abstract: We present an explicit expression for the $q$-difference system, which the $BC_1$-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 Gustafson and the product formula of the $q$-integral introduced by Nassrallah–Rahman and Gustafson.
Keywords: $q$-difference equations; Jackson integral of type $BC_1$; Gustafson’s $C_n$-type sum; Nassrallah–Rahman integral.
Received: December 1, 2008; in final form March 18, 2009; Published online April 3, 2009
Bibliographic databases:
Document Type: Article
MSC: 33D15; 33D67; 39A13
Language: English
Citation: Masahiko Ito, “A First Order $q$-Difference System for the $BC_1$-Type Jackson Integral and Its Applications”, SIGMA, 5 (2009), 041, 14 pp.
Citation in format AMSBIB
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\by Masahiko Ito
\paper A~First Order $q$-Difference System for the $BC_1$-Type Jackson Integral and Its Applications
\jour SIGMA
\yr 2009
\vol 5
\papernumber 041
\totalpages 14
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    • This publication is cited in the following 6 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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