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Varying discrete Laguerre-Sobolev orthogonal polynomials: Asymptotic behavior and zeros

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URI: https://hdl.handle.net/10016/23267
ISSN: 0096-3003
DOI: 10.1016/j.amc.2013.07.074
UXXI: AR/0000014283
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varying_AMC_2013_ps.pdf (1.73 MB)
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2013-10-01
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Elsevier
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Abstract
We consider a varying discrete Sobolev inner product involving the Laguerre weight. Our aim is to study the asymptotic properties of the corresponding orthogonal polynomials and of their zeros. We are interested in Mehler-Heine type formulas because they describe the asymptotic differences between these Sobolev orthogonal polynomials and the classical Laguerre polynomials. Moreover, they give us an approximation of the zeros of the Sobolev polynomials in terms of the zeros of other special functions. We generalize some results appeared very recently in the literature for both the varying and non-varying cases.
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Laguerre-Sobolev orthogonal polynomials, Mehler-Heine formulae, Asymptotics, Zeros
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Applied Mathematics and Computation, 222, pp. 612-61
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