Publication: Asymptotics for Laguerre-Sobolev type orthogonal polynomials modified within their oscillatory regime
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2014-06-01
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Tutors
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Elsevier
Abstract
In this paper we consider sequences of polynomials orthogonal with respect to the discrete Sobolev inner product
(f.g)_s ∫_°^∞ f(x)g(x) x^(α ) e dx+F(c)ΑG(c)^t, α> 1
where f and g are polynomials with real coefficients A∈ R^2.2 and the vectors F(c), G(c) are
A=(■(M&0@0&N)), F(c)=(f(c),f'(c) ) G(c)=(g(c),g'(c))
with M,N ∈ R and the mass point c is located inside the oscillatory region for the classical
Laguerre polynomials. We focus our attention on the representation of these polynomials
in terms of classical Laguerre polynomials and we analyze the behavior of the coefficients
of the corresponding five term recurrence relation when the degree of the polynomials is
large enough. Also, the outer relative asymptotics of the Laguerre Sobolev type with re
spect to the Laguerre polynomials is analyzed.
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Keywords
Orthogonal polynomials, Discrete Sobolev polynomials, Laguerre polynomials, Asymptotics
Bibliographic citation
Applied Mathematics and Computation, 2014, v. 236, pp. 260-272