The Laguerre-Sobolev-type orthogonal polynomials

In this paper we find the second order linear differential equation satisfied by orthogonal polynomials with respect to the inner product p, q = ∞ 0 p(x)q(x)xα e−x dx + Mp(0)q(0) + Np (0)q (o) where α > −1, M ∈ R+ , and p, q are polynomials with real coefficients. We also find some numerical results concerning the distribution of their zeros and their electrostatic interpretation in terms of a logarithmic potential with an external field. We deduce the hypergeometric expression of these polynomials. Finally, the analysis of asymptotic behavior of such polynomials is presented. AMS Subject Classification: 33C47 Key Words and Phrases: Orthogonal polynomials, Laguerre Polynomials, Holonomic Equation, Zeros, Logarithmic potential.

• Type: Journal
• Year: 2010
• Where: JAT
• Authors: Herbert Dueñas, Francisco Marcellán
• Keywords: JAT 2010, Logarithmic Potential, Orthogonal Polynomials, Polynomials