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Asymptotic properties of generalized Laguerre orthogonal polynomials. (English) Zbl 1064.41022
The Laguerre polynomials considered in this paper are orthogonal with respect to a Sobolev inner product. New asymptotic properties of these polynomials are given, together with a limit relation between the zeros of the polynomials and the zeros of a Bessel function. The results are obtained by writing the generalized polynomials as a sum of three classical Laguerre polynomials. Numerical examples illustrate the approximations of the zeros.

MSC:
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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