-Selberg Integrals and Koornwinder Polynomials
We prove a generalization of the -Selberg integral evaluation formula. The integrand is that of a -Selberg integral multiplied by a factor of the same form with respect to part of the variables. The proof relies on the quadratic norm formula of Koornwinder polynomials. We also derive generalizations...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2022 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211531 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | -Selberg Integrals and Koornwinder Polynomials. Jyoichi Kaneko. SIGMA 18 (2022), 014, 35 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We prove a generalization of the -Selberg integral evaluation formula. The integrand is that of a -Selberg integral multiplied by a factor of the same form with respect to part of the variables. The proof relies on the quadratic norm formula of Koornwinder polynomials. We also derive generalizations of Mehta's integral formula as limit cases of our integral.
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| ISSN: | 1815-0659 |