Dual addition formulas associated with dual product formulas
| Autor: | Koornwinder, T.H., Zuhair Nashed, M., Li, X. |
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| Přispěvatelé: | Analysis (KDV, FNWI) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Gegenbauer polynomials Discrete orthogonal polynomials Mathematical analysis Mathematics::Classical Analysis and ODEs Mehler–Heine formula Classical orthogonal polynomials symbols.namesake Difference polynomials Wilson polynomials Orthogonal polynomials symbols Jacobi polynomials Mathematics |
| Zdroj: | Frontiers In Orthogonal Polynomials and Q-series, 373-392 STARTPAGE=373;ENDPAGE=392;TITLE=Frontiers In Orthogonal Polynomials and Q-series |
| ISSN: | 2591-7668 |
| Popis: | We observe that the linearization coefficients for ultraspherical polynomials are the orthogonality weights for Racah polynomials with special parameters. Then it turns out that the linearization sum with such a Racah polynomial as extra factor inserted, can also be evaluated. The corresponding Fourier--Racah expansion is an addition type formula which is dual to the well-known addition formula for ultraspherical polynomials. The limit to the case of Hermite polynomials of this dual addition formula is also considered. Similar results as for ultraspherical polynomials, although only formal, are given by taking the Ruijsenaars--Hallnas dual product formula for Gegenbauer functions as a starting point and by working with Wilson polynomials. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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