The Laguerre-Sobolev-type orthogonal polynomials

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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.
Herbert Dueñas, Francisco Marcellán
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JAT
Authors Herbert Dueñas, Francisco Marcellán
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