Simultaneous pade approximation and orthogonality

Bruin, Marcel G. de

doi:10.1007/bfb0076532

Cited by 46 publications

(26 citation statements)

References 4 publications

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“…This notion has many applications in various domains of mathematics as analytic number theory, approximation theory, special functions theory, and spectral theory of operators (see, for instance, [20]). A convenient framework to discuss explicit examples consists of considering a subclass of multiple orthogonal polynomials known as d-orthogonal polynomials, introduced by Van Iseghem [35] and completed by Maroni [29] as follows.…”

Section: Introductionmentioning

confidence: 99%

Some generalized hypergeometric d-orthogonal polynomial sets

Cheikh

Ouni²

2008

Journal of Mathematical Analysis and Applications

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In this paper, we characterize the d-orthogonal polynomial sets given by their explicit expressions in a specific basis. As application, we consider the generalized hypergeometric case to characterize d-orthogonal polynomial sets of Laguerre type, Meixner type, Meixner-Pollaczek type, Krawtchouk type, continuous dual Hahn type, and dual Hahn type. For d = 1, we obtain a unification of some characterization theorems in the orthogonal polynomials theory.

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Section: Introductionmentioning

confidence: 99%

Some generalized hypergeometric d-orthogonal polynomial sets

Cheikh

Ouni²

2008

Journal of Mathematical Analysis and Applications

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“…The multiple orthogonal polynomials were developed in Hermite-Padé approximation in order to get a simultaneous rational approximant. See [1,4,7,8,11,14,18] and references therein. Recently the multiple OPS attracted many interests as an extension of ordinary orthogonal polynomials [2,3,6,10,17].…”

Section: Introductionmentioning

confidence: 99%

Difference equations for discrete classical multiple orthogonal polynomials

Lee¹

2008

Journal of Approximation Theory

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For discrete multiple orthogonal polynomials such as the multiple Charlier polynomials, the multiple Meixner polynomials, and the multiple Hahn polynomials, we first find a lowering operator and then give a (r + 1)th order difference equation by combining the lowering operator with the raising operator. As a corollary, explicit third order difference equations for discrete multiple orthogonal polynomials are given, which was already proved by Van Assche for the multiple Charlier polynomials and the multiple Meixner polynomials.

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“…In this paper r will always represent the number of weights. Multiple orthogonal polynomials arise naturally in the theory of simultaneous rational approximation, in particular in Hermite-Padé approximation of a system of r (Markov) functions [6,7,20].…”

Section: Introductionmentioning

confidence: 99%

Multiple Wilson and Jacobi–Piñeiro polynomials

Beckermann

Coussement

Assche

2005

Journal of Approximation Theory

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We introduce multiple Wilson polynomials, which give a new example of multiple orthogonal polynomials (Hermite-Padé polynomials) of type II. These polynomials can be written as a Jacobi-Piñeiro transform, which is a generalization of the Jacobi transform for Wilson polynomials, found by Koornwinder. Here we need to introduce Jacobi and Jacobi-Piñeiro polynomials with complex parameters. Some explicit formulas are provided for both Jacobi-Piñeiro and multiple Wilson polynomials, one of them in terms of Kampé de Fériet series. Finally, we look at some limiting relations and construct a part of a multiple AT-Askey table.

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Simultaneous pade approximation and orthogonality

Cited by 46 publications

References 4 publications

Some generalized hypergeometric d-orthogonal polynomial sets

Some generalized hypergeometric d-orthogonal polynomial sets

Difference equations for discrete classical multiple orthogonal polynomials

Multiple Wilson and Jacobi–Piñeiro polynomials

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