Abstract

DUENAS, HERBERT; GARCIA, JUAN C.; GARZA, LUIS E.  and  RAMIREZ, ALEJANDRO. The Diagonal General Case of the Laguerre-Sobolev Type Orthogonal Polynomials. Rev.colomb.mat. [online]. 2013, vol.47, n.1, pp.39-66. ISSN 0034-7426.

We consider the family of polynomials orthogonal with respect to the Sobolev type inner product corresponding to the diagonal general case of the Laguerre-Sobolev type orthogonal polynomials. We analyze some properties of these polynomials, such as the holonomic equation that they satisfy and, as an application, an electrostatic interpretation of their zeros. We also obtain a representation of such polynomials as a hypergeometric function, and study the behavior of their zeros.

Keywords : Orthogonal polynomials; Laguerre-Sobolev type polynomials; Laguerre Polynomials; Derivative of a Dirac Delta.

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