Connection Formula for the Jackson Integral of Type An and Elliptic Lagrange Interpolation
We investigate the connection problem for the Jackson integral of type An. Our connection formula implies a Slater-type expansion of a bilateral multiple basic hypergeometric series as a linear combination of several specific multiple series. Introducing certain elliptic Lagrange interpolation funct...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2018 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209773 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Connection Formula for the Jackson Integral of Type An and Elliptic Lagrange Interpolation / M. Ito, M. Noumi // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 35 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862549347987619840 |
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| author | Ito, M. Noumi, M. |
| author_facet | Ito, M. Noumi, M. |
| citation_txt | Connection Formula for the Jackson Integral of Type An and Elliptic Lagrange Interpolation / M. Ito, M. Noumi // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 35 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We investigate the connection problem for the Jackson integral of type An. Our connection formula implies a Slater-type expansion of a bilateral multiple basic hypergeometric series as a linear combination of several specific multiple series. Introducing certain elliptic Lagrange interpolation functions, we determine the explicit form of the connection coefficients. We also use basic properties of the interpolation functions to establish an explicit determinant formula for a fundamental solution matrix of the associated system of q-difference equations.
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| first_indexed | 2025-12-03T21:41:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209773 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-03T21:41:17Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ito, M. Noumi, M. 2025-11-26T11:34:08Z 2018 Connection Formula for the Jackson Integral of Type An and Elliptic Lagrange Interpolation / M. Ito, M. Noumi // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 35 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D52; 39A13 arXiv: 1801.07041 https://nasplib.isofts.kiev.ua/handle/123456789/209773 https://doi.org/10.3842/SIGMA.2018.077 We investigate the connection problem for the Jackson integral of type An. Our connection formula implies a Slater-type expansion of a bilateral multiple basic hypergeometric series as a linear combination of several specific multiple series. Introducing certain elliptic Lagrange interpolation functions, we determine the explicit form of the connection coefficients. We also use basic properties of the interpolation functions to establish an explicit determinant formula for a fundamental solution matrix of the associated system of q-difference equations. The authors would like to express their gratitude to the referees for providing them with many useful suggestions. This work is supported by JSPS Kakenhi Grants (C)25400118, (B)15H03626, and (C)18K03339. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Connection Formula for the Jackson Integral of Type An and Elliptic Lagrange Interpolation Article published earlier |
| spellingShingle | Connection Formula for the Jackson Integral of Type An and Elliptic Lagrange Interpolation Ito, M. Noumi, M. |
| title | Connection Formula for the Jackson Integral of Type An and Elliptic Lagrange Interpolation |
| title_full | Connection Formula for the Jackson Integral of Type An and Elliptic Lagrange Interpolation |
| title_fullStr | Connection Formula for the Jackson Integral of Type An and Elliptic Lagrange Interpolation |
| title_full_unstemmed | Connection Formula for the Jackson Integral of Type An and Elliptic Lagrange Interpolation |
| title_short | Connection Formula for the Jackson Integral of Type An and Elliptic Lagrange Interpolation |
| title_sort | connection formula for the jackson integral of type an and elliptic lagrange interpolation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209773 |
| work_keys_str_mv | AT itom connectionformulaforthejacksonintegraloftypeanandellipticlagrangeinterpolation AT noumim connectionformulaforthejacksonintegraloftypeanandellipticlagrangeinterpolation |