Differential equations for multiple orthogonal polynomials with respect to classical weights: raising and lowering operators

Coussement, J.; Assche, Walter Van

doi:10.1088/0305-4470/39/13/010

Cited by 17 publications

(21 citation statements)

References 10 publications

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“…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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“…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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“…In [12], differential equations for multiple Hermite polynomials and multiple Laguerre polynomials were reconstructed using the generating functions. Recently, Coussement and Van Assche [5] found again the (r + 1)th order differential equations for multiple OPS's, except multiple Bessel polynomials, using lowering and raising operators.…”

Section: Introductionmentioning

confidence: 99%

A Differential Equation for Multiple Bessel Polynomials With Raising and Lowering Operators

Baek¹,

Lee²

2011

Bulletin of the Korean Mathematical Society

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“…Recently multiple orthogonal polynomials were extensively studied in a special function theory, in number theory, in approximation theory, and so on ( [6,7,11,13,14,19,21,22]). But there do not exist characterization theorems to specify a class of multiple orthogonal polynomials (in the general case), as far as the author knows.…”

Section: Introductionmentioning

confidence: 99%