dorsal/arxiv
View SchemaZeros and orthogonality of the Askey-Wilson polynomials for q a root of unity
| Authors | V. Spiridonov, A. Zhedanov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9605034 |
| URL | https://arxiv.org/abs/q-alg/9605034 |
| Journal | Duke Math. J. 89 (1997), 283--305 |
Abstract
We study some properties of the Askey-Wilson polynomials (AWP) when q is a primitive N-th root of unity. For general four-parameter AWP, zeros of the N-th polynomial and the orthogonality measure are found explicitly. Special subclasses of the AWP, e.g., the continuous q-Jacobi and big q-Jacobi polynomials, are considered in detail. A set of discrete weight functions positive on a real interval is described. Some new trigonometric identities related to the AWP are obtained. Normalization conditions of some polynomials are expressed in terms of the Gauss sums.
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"abstract": "We study some properties of the Askey-Wilson polynomials (AWP) when q is a\nprimitive N-th root of unity. For general four-parameter AWP, zeros of the N-th\npolynomial and the orthogonality measure are found explicitly. Special\nsubclasses of the AWP, e.g., the continuous q-Jacobi and big q-Jacobi\npolynomials, are considered in detail. A set of discrete weight functions\npositive on a real interval is described. Some new trigonometric identities\nrelated to the AWP are obtained. Normalization conditions of some polynomials\nare expressed in terms of the Gauss sums.",
"arxiv_id": "q-alg/9605034",
"authors": [
"V. Spiridonov",
"A. Zhedanov"
],
"categories": [
"q-alg",
"math.QA"
],
"journal_ref": "Duke Math. J. 89 (1997), 283--305",
"title": "Zeros and orthogonality of the Askey-Wilson polynomials for q a root of unity",
"url": "https://arxiv.org/abs/q-alg/9605034"
},
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