Dual addition formulas: the case of continuous $q$-ultraspherical and $q$-Hermite polynomials
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866914733546799104 |
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| author | Koornwinder, Tom H. |
| author_facet | Koornwinder, Tom H. |
| contents | We settle the dual addition formula for continuous $q$-ultraspherical polynomials as an expansion in terms of special $q$-Racah polynomials for which the constant term is given by the linearization formula for the continuous $q$-ultraspherical polynomials. In a second proof we derive the dual addition formula from the Rahman--Verma addition formula for these polynomials by using the self-duality of the polynomials. We also consider the limit case of continuous $q$-Hermite polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_09636 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Dual addition formulas: the case of continuous $q$-ultraspherical and $q$-Hermite polynomials Koornwinder, Tom H. Classical Analysis and ODEs 33.D45 We settle the dual addition formula for continuous $q$-ultraspherical polynomials as an expansion in terms of special $q$-Racah polynomials for which the constant term is given by the linearization formula for the continuous $q$-ultraspherical polynomials. In a second proof we derive the dual addition formula from the Rahman--Verma addition formula for these polynomials by using the self-duality of the polynomials. We also consider the limit case of continuous $q$-Hermite polynomials. |
| title | Dual addition formulas: the case of continuous $q$-ultraspherical and $q$-Hermite polynomials |
| topic | Classical Analysis and ODEs 33.D45 |
| url | https://arxiv.org/abs/1803.09636 |