Asymptotic properties of generalized Laguerre orthogonal polynomials

Álvarez-Nodarse, R.; Moreno-Balcázar, Juan J.

doi:10.1016/s0019-3577(04)90012-2

Cited by 32 publications

(47 citation statements)

References 16 publications

(39 reference statements)

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“…Later on in [6] asymptotic properties of the zeros were looked for. So MehlerHeine type formulas were obtained and therefore limit relations between the zeros of generalized Laguerre polynomials and the zeros of Bessel functions were also deduced.…”

Section: A Generalization Of Laguerre Polynomials: the Laguerre-sobolmentioning

confidence: 99%

“…In [6] a conjecture was stated for the polynomials L (α,M0,...,Ms) n (x) orthogonal with respect to the inner product…”

Section: A Generalization Of Laguerre Polynomials: the Laguerre-sobolmentioning

confidence: 99%

“…. for the Sobolev polynomials orthogonal with respect to (25) where the measures are given by (6) and (7), respectively.…”

Section: Hermite Weightsmentioning

confidence: 99%

“…6 for the Laguerre case. In fact, the possibility of one negative zero for Laguerre-Sobolev polynomials of case II is, in some sense, equivalent to the possibility of two conjugate complex zeros for even Hermite-Sobolev polynomials of case II.…”

Section: Zeros and Its Asymptoticsmentioning

confidence: 99%

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Asymptotics and Zeros of Sobolev Orthogonal Polynomials on Unbounded Supports

Marcellán

Moreno-Balcázar

2006

Acta Appl Math

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In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we focus on the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some directions for future research are formulated.MSC: Primary 42C05; Secondary 33C45

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Section: A Generalization Of Laguerre Polynomials: the Laguerre-sobolmentioning

confidence: 99%

“…In [6] a conjecture was stated for the polynomials L (α,M0,...,Ms) n (x) orthogonal with respect to the inner product…”

Section: A Generalization Of Laguerre Polynomials: the Laguerre-sobolmentioning

confidence: 99%

“…. for the Sobolev polynomials orthogonal with respect to (25) where the measures are given by (6) and (7), respectively.…”

Section: Hermite Weightsmentioning

confidence: 99%

Section: Zeros and Its Asymptoticsmentioning

confidence: 99%

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Asymptotics and Zeros of Sobolev Orthogonal Polynomials on Unbounded Supports

Marcellán

Moreno-Balcázar

2006

Acta Appl Math

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“…The case j = 1 has attracted the interest of many researchers from many points of view. First, the analysis of the asymptotic properties of such orthogonal polynomials is done (see [1] and the survey paper [10]). Second, the study of analytic properties of their zeros such as interlacing with the zeros of Laguerre polynomials and monotonicity of each zero in terms of N, among others, are completely discussed in [4].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Monotonicity and asymptotics of zeros of Laguerre-Sobolev-type orthogonal polynomials of higher order derivatives

Marcellán

Rafaeli

2011

Proc. Amer. Math. Soc.

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Abstract.In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner productwhere α > −1, N ≥ 0, and j ∈ N. In particular, we focus our attention on their interlacing properties with respect to the zeros of Laguerre polynomials as well as on the monotonicity of each individual zero in terms of the mass N. Finally, we give necessary and sufficient conditions in terms of N in order for the least zero of any Laguerre-Sobolev-type orthogonal polynomial to be negative.

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