$q$-Selberg extensions of Gasper's two stage $q$-beta integrals
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913177024856064 |
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| author | Ito, Masahiko Forrester, Peter J. |
| author_facet | Ito, Masahiko Forrester, Peter J. |
| contents | Gasper gave a two-step extension of the Askey-Roy formula for a beta-integral type defined on the unit circle. This involved increasing the number of parameters and adding a balancing condition. We derive a multidimensional generalization of the final formula in Gasper's extension. By considering a two-step degeneration involving parameters our generalization becomes Tarasov-Varchenko's formula -- itself a multidimensional generalization of the original Askey-Roy formula. The proof is done by Aomoto's method. This generalized integration by parts strategy makes use of a class of functions known as the fundamental invariants of type $BC$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01140 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $q$-Selberg extensions of Gasper's two stage $q$-beta integrals Ito, Masahiko Forrester, Peter J. Complex Variables Classical Analysis and ODEs Gasper gave a two-step extension of the Askey-Roy formula for a beta-integral type defined on the unit circle. This involved increasing the number of parameters and adding a balancing condition. We derive a multidimensional generalization of the final formula in Gasper's extension. By considering a two-step degeneration involving parameters our generalization becomes Tarasov-Varchenko's formula -- itself a multidimensional generalization of the original Askey-Roy formula. The proof is done by Aomoto's method. This generalized integration by parts strategy makes use of a class of functions known as the fundamental invariants of type $BC$. |
| title | $q$-Selberg extensions of Gasper's two stage $q$-beta integrals |
| topic | Complex Variables Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2606.01140 |