Results 1 to 10 of about 3,264 (278)

Christoffel transform and multiple orthogonal polynomials [PDF]

Journal of Computational and Applied Mathematics
We investigate multiple orthogonal polynomials associated with the system of measures obtained by applying a Christoffel transform to each of the orthogonality measures. We present an algorithm for computing the transformed recurrence coefficients and determinantal formulas for the transformed multiple orthogonal polynomials of type I and type II.
Rostyslav Kozhan, Marcus Vaktnäs
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Orthogonal and Multiple Orthogonal Polynomials, Random Matrices, and Painlevé Equations [PDF]

, 2020
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics and probability and many other disciplines.
Walter Van Assche
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Planar orthogonal polynomials as Type II multiple orthogonal polynomials [PDF]

Journal of Physics A: Mathematical and Theoretical, 2019
We show that the planar orthogonal polynomials with $l$ logarithmic singularities in the potential are the multiple orthogonal polynomials (Hermite-Pad polynomials) of Type II with $l$ measures. We also find the ratio between the determinant of the moment matrix corresponding to the multiple orthogonal polynomials and the determinant of the moment ...
Seung-Yeop Lee, Meng Yang
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Some discrete multiple orthogonal polynomials

Journal of Computational and Applied Mathematics, 2003
27 pages, no figures.-- MSC2000 codes: 33C45, 33C10, 42C05, 41A28.-- Issue title: "Proceedings of the 6th International Symposium on Orthogonal Polynomials, Special Functions and their Applications" (OPSFA-VI, Rome, Italy, 18-22 June 2001). MR#: MR1985676 (2004g:33015) Zbl#: Zbl 1021.33006 In this paper, we extend the theory of discrete orthogonal ...
J. Arvesú, J. Coussement, Walter Van Assche   +2 more
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Gauusian quadrature for multiple orthogonal polynomials [PDF]

Journal of Computational and Applied Mathematics, 2004
We study multiple orthogonal polynomials of type I and type II which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix L_n, containing the recurrence coefficients.
J. Coussement, Walter Van Assche
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Nearest Neighbor Recurrence Relations for Meixner–Angelesco Multiple Orthogonal Polynomials of the Second Kind

Mathematics, 2023
This paper studies a new family of Angelesco multiple orthogonal polynomials with shared orthogonality conditions with respect to a system of weight functions, which are complex analogs of Pascal distributions on a legged star-like set.
Jorge Arvesú, Alejandro J. Quintero Roba   +1 more
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anar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials

Symmetry, Integrability and Geometry: Methods and Applications, 2023
A recent result of S.-Y. Lee and M. Yang states that the planar orthogonal polynomials orthogonal with respect to a modified Gaussian measure are multiple orthogonal polynomials of type II on a contour in the complex plane. We show that the same polynomials are also type I orthogonal polynomials on a contour, provided the exponents in the weight are ...
Berezin, Sergey, Kuijlaars, Arno, Parra, Iván   +2 more
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Multiple big q-Jacobi polynomials [PDF]

Bulletin of Mathematical Sciences, 2020
Here, we investigate type II multiple big q-Jacobi orthogonal polynomials. We provide their explicit formulae in terms of basic hypergeometric series, raising and lowering operators, Rodrigues formulae, third-order q-difference equation, and we obtain ...
Fethi Bouzeffour, Mubariz Garayev
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Poly-Genocchi polynomials and its applications

AIMS Mathematics, 2021
In this paper, we discussed some new properties on the newly defined family of Genocchi polynomials, called poly-Genocchi polynomials. These polynomials are extensions from the Genocchi polynomials via generating function involving polylogarithm function.
Chang Phang, Abdulnasir Isah, Yoke Teng Toh   +2 more
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General Geronimus Perturbations for Mixed Multiple Orthogonal Polynomials [PDF]

Analysis and Mathematical Physics
General Geronimus transformations, defined by regular matrix polynomials that are neither required to be monic nor restricted by the rank of their leading coefficients, are applied through both right and left multiplication to a rectangular matrix of measures associated with mixed multiple orthogonal polynomials.
Manuel Mañas, Miguel Rojas
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