Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights

  • Authors:

  • Cleonice F. Bracciali;Laura Castaño-García;Juan J. Moreno-Balcázar

  • Affiliations:

  • DCCE, IBILCE, UNESP - Univ Estadual Paulista, 15054-000 São José do Rio Preto, SP, Brazil;Dpto de Estadística y Matemática Aplicada, Universidad de Almería, La Cañada de San Urbano s/n, 04120, Almería, Spain;Dpto de Estadística y Matemática Aplicada, Universidad de Almería, La Cañada de San Urbano s/n, 04120, Almería, Spain and Instituto Carlos I de Física Teórica y ...

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2010

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Abstract

We consider the Sobolev inner product =@!"-"1^1f(x)g(x)(1-x^2)^@a^-^1^2dx+@!f^'(x)g^'(x)d@j(x),@a-12, where d@j is a measure involving a Gegenbauer weight and with mass points outside the interval (-1,1). We study the asymptotic behaviour of the polynomials which are orthogonal with respect to this inner product. We obtain the asymptotics of the largest zeros of these polynomials via a Mehler-Heine type formula. These results are illustrated with some numerical experiments.