On asymptotic properties of Laguerre–Sobolev type orthogonal polynomials
- Molano, Luis Alejandro Molano
Publication date
July 2013
DOI Publisher
Production and hosting by Elsevier B.V.Abstract
AbstractIn this paper, we consider the asymptotic behavior of the sequence of monic polynomials orthogonal with respect to the Sobolev inner product〈p,q〉S=∫0∞p(x)q(x)dμ+Mp(m)(ζ)q(m)(ζ),where ζ<0, M⩾0 and dμ=e−xxαdx. We study the outer relative asymptotics of these polynomials with respect to the classical Laguerre polynomials, and we deduce a Mehler–Heine type formula and a Plancherel–Rotach type formula for the rescaled polynomials
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