Results 11 to 20 of about 72,702 (264)
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
Van Assche, W., Yakubovich, S. B.
openaire +4 more sources
Multiple orthogonal polynomials
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 ...
openaire +3 more sources
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 ...
Arvesú, J. +2 more
openaire +4 more sources
Gaussian quadrature for multiple orthogonal polynomials
Journal of Computational and Applied Mathematics, 2005 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.
Coussement, Jonathan, Van Assche, Walter
openaire +4 more sources
Multiple orthogonal polynomials: Pearson equations and Christoffel formulas
Analysis and Mathematical Physics, 2022 AbstractMultiple orthogonal polynomials with respect to two weights on the step-line are considered. A connection between different dual spectral matrices, one banded (recursion matrix) and one Hessenberg, respectively, and the Gauss–Borel factorization of the moment matrix is given. It is shown a hidden freedom exhibited by the spectral system related
Amílcar Branquinho +2 more
openaire +7 more sources
A Christoffel–Darboux formula for multiple orthogonal polynomials
Journal of Approximation Theory, 2004 11 pages, no ...
Daems, E., Kuijlaars, A.B.J.
openaire +5 more sources
Average characteristic polynomials for multiple orthogonal polynomial ensembles
Journal of Approximation Theory, 2010 Multiple orthogonal polynomials (MOP) are a non-definite version of matrix orthogonal polynomials. They are described by a Riemann-Hilbert matrix Y consisting of four blocks Y_{1,1}, Y_{1,2}, Y_{2,1} and Y_{2,2}. In this paper, we show that det Y_{1,1} (det Y_{2,2}) equals the average characteristic polynomial (average inverse characteristic polynomial,
openaire +5 more sources
On the ω-multiple Charlier polynomials
Advances in Difference Equations, 2021 The main aim of this paper is to define and investigate more general multiple Charlier polynomials on the linear lattice ω N = { 0 , ω , 2 ω , … } $\omega \mathbb{N} = \{ 0,\omega ,2\omega ,\ldots \} $ , ω ∈ R $\omega \in \mathbb{R}$ .
Mehmet Ali Özarslan, Gizem Baran
doaj +1 more source
Angular Correlation Using Rogers-Szegő-Chaos
Mathematics, 2020 Polynomial chaos expresses a probability density function (pdf) as a linear combination of basis polynomials. If the density and basis polynomials are over the same field, any set of basis polynomials can describe the pdf; however, the most logical ...
Christine Schmid, Kyle J. DeMars
doaj +1 more source
Numerical solution of neutral delay differential equations using orthogonal neural network
Scientific Reports, 2023 In this paper, an efficient orthogonal neural network (ONN) approach is introduced to solve the higher-order neutral delay differential equations (NDDEs) with variable coefficients and multiple delays.
Chavda Divyesh Vinodbhai, Shruti Dubey
doaj +1 more source