Results 11 to 20 of about 71,161 (303)
What is $\ldots\ $ a multiple orthogonal polynomial? [PDF]
Notices of the American Mathematical Society, 2016 This is an extended version of our note in the Notices of the American Mathematical Society 63 (2016), no. 9, in which we explain what multiple orthogonal polynomials are and where they appear in various applications.Comment: 5 pages, 2 ...
Martínez-Finkelshtein, Andrei +1 more
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On the q-Charlier Multiple Orthogonal Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2015 We introduce a new family of special functions, namely q-Charlier multiple orthogonal polynomials. These polynomials are orthogonal with respect to q-analogues of Poisson distributions. We focus our attention on their structural properties.
Arvesú, Jorge +1 more
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Mehler-Heine asymptotics for multiple orthogonal polynomials [PDF]
Proceedings of the American Mathematical Society, 2016 Mehler-Heine asymptotics describe the behavior of orthogonal polynomials near the edges of the interval where the orthogonality measure is supported. For Jacobi polynomials and Laguerre polynomials this asymptotic behavior near the hard edge involves ...
Van Assche, Walter
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Computing recurrence coefficients of multiple orthogonal polynomials [PDF]
Numerical Algorithms, 2015 Multiple orthogonal polynomials satisfy a number of recurrence relations, in particular there is a $(r+2)$-term recurrence relation connecting the type II multiple orthogonal polynomials near the diagonal (the so-called step-line recurrence relation) and
Filipuk, Galina +2 more
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Multiple orthogonal polynomials [PDF]
Journal of Computational and Applied Mathematics, 1998 This is a review of the advances in the theory of simultaneous Padé approximants for the past five years. It covers new results in the classification of what appear to be the semiclassical multiple orthogonal polynomials, new applications to number theory, connections with the spectral theory of non-symmetric operators and orthogonal polynomials with ...
Alexander Ivanovich Aptekarev
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Multiple orthogonal polynomials for classical weights [PDF]
Transactions of the American Mathematical Society, 2003 A new set of special functions, which has a wide range of applications from number theory to integrability of nonlinear dynamical systems, is described. The multiple orthogonal polynomials with respect to \(p>1\) weights satisfying Pearson's equation. In particular, a classification of multiple orthogonal polynomials with respect to classical weights ...
Alexander Ivanovich Aptekarev +2 more
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Christoffel functions for multiple orthogonal polynomials [PDF]
Journal of Approximation Theory, 2022 We study weak asymptotic behaviour of the Christoffel--Darboux kernel on the main diagonal corresponding to multiple orthogonal polynomials. We show that under some hypotheses the weak limit of $\tfrac{1}{n} K_n(x,x)\, dμ$ is the same as the limit of the normalized zero counting measure of type II multiple orthogonal polynomials.
Grzegorz Świderski, Walter Van Assche
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Strong asymptotics for the Pollaczek multiple orthogonal polynomials [PDF]
Doklady Mathematics, 2014 The asymptotic properties of multiple orthogonal polynomials with respect to two Pollaczek weights with different parameters are considered. This set of weights is a Nikishin system generated by two measures with unbounded supports; moreover, the second ...
Aptekarev, A. I. +2 more
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Some discrete multiple orthogonal polynomials
Journal of Computational and Applied Mathematics, 2003 Zbl#: Zbl 1021 ...
J. Arvesú +2 more
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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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