A family of orthogonal functions on the unit circle and a new multilateral matrix inverse
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913912630280192 |
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| author | Schlosser, Michael J. |
| author_facet | Schlosser, Michael J. |
| contents | Using Bailey's very-well-poised $_6ψ_6$ summation, we show that a specific sequence of well-poised bilateral basic hypergeometric $_3ψ_3$ series form a family of orthogonal functions on the unit circle. We further extract a bilateral matrix inverse from Dougall's ${}_2H_2$ summation which we use, in combination with the Pfaff--Saalschütz summation, to derive a summation for a particular bilateral hypergeometric $_3H_3$ series. We finally provide multivariate extensions of the bilateral matrix inverse and the $_3H_3$ summation in the setting of hypergeometric series associated to the root system $A_r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03559 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A family of orthogonal functions on the unit circle and a new multilateral matrix inverse Schlosser, Michael J. Classical Analysis and ODEs Combinatorics Quantum Algebra 33D45 (Primary) 15A05, 33C20, 33D15, 33C67, 33D67 (Secondary) Using Bailey's very-well-poised $_6ψ_6$ summation, we show that a specific sequence of well-poised bilateral basic hypergeometric $_3ψ_3$ series form a family of orthogonal functions on the unit circle. We further extract a bilateral matrix inverse from Dougall's ${}_2H_2$ summation which we use, in combination with the Pfaff--Saalschütz summation, to derive a summation for a particular bilateral hypergeometric $_3H_3$ series. We finally provide multivariate extensions of the bilateral matrix inverse and the $_3H_3$ summation in the setting of hypergeometric series associated to the root system $A_r$. |
| title | A family of orthogonal functions on the unit circle and a new multilateral matrix inverse |
| topic | Classical Analysis and ODEs Combinatorics Quantum Algebra 33D45 (Primary) 15A05, 33C20, 33D15, 33C67, 33D67 (Secondary) |
| url | https://arxiv.org/abs/2412.03559 |