¹Universidad Nacional de Colombia, Bogotá, Colombia. Email: haduenasr@unal.edu.co
²Universidad Nacional de Colombia, Bogotá, Colombia. Email: jcgarciaar@unal.edu.co
³Universidad de Colima, Colima, México. Email: garzaleg@gmail.com
⁴Universidad de Colima, Colima, México. Email: grarceo@gmail.com

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.

Key words: Orthogonal polynomials, Laguerre-Sobolev type polynomials, Laguerre Polynomials, Derivative of a Dirac Delta.

Se considera la familia de los polinomios ortogonales con respecto a un producto interno de tipo Sobolev correspondiente al caso general diagonal de los polinomios ortogonales de tipo Laguerre-Sobolev. Se analizan algunas propiedades de estos polinomios tales como la ecuación holonómica que satisfacen y, como una aplicación de dicha ecuación, una interpretación electrostática de sus ceros. También se obtiene una representación de tales polinomios en términos de una función hipergeométrica, y se estudia el comportamiento de sus ceros.

Palabras clave: Polinomios ortogonales, polinomios de tipo Laguerre-Sobolev, polinomios de Laguerre, derivada de una Delta de Dirac.

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References

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