A First Order q-Difference System for the BC₁-Type Jackson Integral and Its Applications
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2009 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149165 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862538108379070464 |
|---|---|
| author | Ito, M. |
| author_facet | Ito, M. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 Gustafson and the product formula of the q-integral introduced by Nassrallah-Rahman and Gustafson.
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| first_indexed | 2025-11-24T12:51:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149165 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T12:51:25Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ito, M. 2019-02-19T17:53:29Z 2019-02-19T17:53:29Z 2009 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. 1815-0659 2000 Mathematics Subject Classification: 33D15; 33D67; 39A13 https://nasplib.isofts.kiev.ua/handle/123456789/149165 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 Gustafson and the product formula of the q-integral introduced by Nassrallah-Rahman and Gustafson. This paper is a contribution to the Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions” (July 21–25, 2008, MPIM, Bonn, Germany). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A First Order q-Difference System for the BC₁-Type Jackson Integral and Its Applications Article published earlier |
| spellingShingle | A First Order q-Difference System for the BC₁-Type Jackson Integral and Its Applications Ito, M. |
| title | A First Order q-Difference System for the BC₁-Type Jackson Integral and Its Applications |
| title_full | A First Order q-Difference System for the BC₁-Type Jackson Integral and Its Applications |
| title_fullStr | A First Order q-Difference System for the BC₁-Type Jackson Integral and Its Applications |
| title_full_unstemmed | A First Order q-Difference System for the BC₁-Type Jackson Integral and Its Applications |
| title_short | A First Order q-Difference System for the BC₁-Type Jackson Integral and Its Applications |
| title_sort | first order q-difference system for the bc₁-type jackson integral and its applications |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149165 |
| work_keys_str_mv | AT itom afirstorderqdifferencesystemforthebc1typejacksonintegralanditsapplications AT itom firstorderqdifferencesystemforthebc1typejacksonintegralanditsapplications |