Differential equations for discrete Laguerre–Sobolev orthogonal polynomials

• Antonio J. Durán ^[1] ; Manuel D. de la Iglesia ^[1]
  1. [1] Universidad de Sevilla

     Universidad de Sevilla

     Sevilla, España

     
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 195, Nº 1 (July 2015), 2015, págs. 70-88
• Idioma: inglés
• DOI: 10.1016/j.jat.2014.01.004
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• Resumen

  • The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Laguerre–Sobolev bilinear form with mass point at zero. In particular we construct the orthogonal polynomials using certain Casorati determinants. Using this construction, we prove that they are eigenfunctions of a differential operator (which will be explicitly constructed). Moreover, the order of this differential operator is explicitly computed in terms of the matrix which defines the discrete Laguerre–Sobolev bilinear form.