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Zeros of Gegenbauer and Hermite polynomials and connection coefficients |
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| Authors: | Ivá n Area Dimitar K Dimitrov Eduardo Godoy André Ronveaux |
| Institution: | Departamento de Matemática Aplicada II, E.T.S.E. Telecomunicación, Universidade de Vigo, Campus Lagoas--Marcosende, 36200 Vigo, Spain ; Departamento de Ciências de Computação e Estatística, IBILCE, Universidade Estadual Paulista, 15054-000 São José do Rio Preto, SP, Brazil ; Departamento de Matemática Aplicada II, E.T.S.I. Industriales, Universidade de Vigo, Campus Lagoas--Marcosende, 36200 Vigo, Spain ; Departement de Mathematique, Unité D'Analyse Mathématique et de Mécanique, Université Catholique de Louvain, Bâtiment Marc de Hemptinne, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium |
| Abstract: | In this paper, sharp upper limit for the zeros of the ultraspherical polynomials are obtained via a result of Obrechkoff and certain explicit connection coefficients for these polynomials. As a consequence, sharp bounds for the zeros of the Hermite polynomials are obtained. |
| Keywords: | Orthogonal polynomials zeros of Gegenbauer polynomials zeros of Hermite polynomials connection coefficients |
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