Results 21 to 30 of about 71,161 (303)
On Certain Wronskians of Multiple Orthogonal Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2014 We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians keep a constant sign in some cases, while in some other cases ...
Lun Zhang
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Multiple orthogonal polynomials associated with the exponential integral [PDF]
Studies in Applied Mathematics, 2023 AbstractWe introduce a new family of multiple orthogonal polynomials satisfying orthogonality conditions with respect to two weights on the positive real line, with the gamma density and a density related to the exponential integral . We give explicit formulas for the type I functions and type II polynomials, their Mellin transform, Rodrigues ...
Walter Van Assche, Thomas Wolfs
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Some classical multiple orthogonal polynomials [PDF]
Journal of Computational and Applied Mathematics, 2001 Recently there has been a renewed interest in an extension of the notion of orthogonal polynomials known as multiple orthogonal polynomials. This notion comes from simultaneous rational approximation (Hermite-Pade approximation) of a system of several functions.
Walter Van Assche, Els Coussement
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Global fluctuations for Multiple Orthogonal Polynomial Ensembles
Journal of Functional Analysis, 2021 We study the fluctuations of linear statistics with polynomial test functions for Multiple Orthogonal Polynomial Ensembles. Multiple Orthogonal Polynomial Ensembles form an important class of determinantal point processes that include random matrix models such as the GUE with external source, complex Wishart matrices, multi-matrix models and others ...
Maurice Duits +2 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 +2 more
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The Symmetrization Problem for Multiple Orthogonal Polynomials [PDF]
, 2021 We analyze the effect of symmetrization in the theory of multiple orthogonal polynomials. For a symmetric sequence of type II multiple orthogonal polynomials satisfying a high-term recurrence relation, we fully characterize the Weyl function associated to the corresponding block Jacobi matrix as well as the Stieltjes matrix function.
Amílcar Branquinho, Edmundo J. Huertas
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Gauusian quadrature for multiple orthogonal polynomials
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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Multiple orthogonal polynomials associated with macdonald functions [PDF]
Integral Transforms and Special Functions, 2000 We consider multiple orthogonal polynomials corresponding to two Macdonald functions (modified Bessel functions of the second kind), with emphasis on the polynomials on the diagonal of the Hermite-Pad table. We give some properties of these polynomials: differential properties, a Rodrigues type formula and explicit formulas for the third order linear
Walter Van Assche, Semyon Yakubovich
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On relation between one multiple and a corresponding one-dimensional integral with applications [PDF]
Yugoslav Journal of Operations Research, 2018 For a given finite positive measure on an interval I ⊆ R, a multiple stochastic integral of a Volterra kernel with respect to a product of a corresponding Gaussian orthogonal stochastic measure is introduced.
Bajić Tatjana
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Multiple Meixner Polynomials on a Non-Uniform Lattice
Mathematics, 2020 We consider two families of type II multiple orthogonal polynomials. Each family has orthogonality conditions with respect to a discrete vector measure.
Jorge Arvesú +1 more
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