IJPAM: Volume 38, No. 3 (2007)

LAGUERRE-TYPE ORTHOGONAL POLYNOMIALS:
ELECTROSTATIC INTERPRETATION

Herbert Dueñas$^{1,2}$, Francisco Marcellán$^2$
$^1$Departamento de Matemáticas
Universidad Nacional de Colombia
Ciudad Universitaria, Bogotá, COLOMBIA
e-mail: haduenasr@unal.edu.co
$^2$Departamento de Matemáticas
Universidad Carlos III de Madrid
Avenida de la Universidad 30, Leganés, 28911, SPAIN
e-mail: pacomarc@ing.uc3m.es


Abstract.In this contribution we study the second order linear differential equation satisfied by polynomials orthogonal with respect to the linear functional \begin{equation*}
\left\langle \widetilde{\mu } ,p\right\rangle
=\int_{0}^{+\infty}p(x)x^{\alpha }e^{-x}dx+Mp(0)\,,
\end{equation*} where $\alpha >-1,$ $M\in \mathbb{R}_{+}$ , and $p$ is a polynomial with real coefficients. We also find some results concerning the distribution of their zeros. Finally, an electrostatic interpretation of the zeros in terms of a logarithmic potential with an external field is presented.

Received: April 4, 2007

AMS Subject Classification: 33C47

Key Words and Phrases: orthogonal polynomials, Laguerre weights, holonomic equation, zeros, logarithmic potential

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 38
Issue: 3