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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 ...
A. I. Aptekarev +2 more
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Algorithms for classical orthogonal polynomials
, 1996 In this article explicit formulas for the recurrence equation p_{n+1}(x) = (A_n x + B_n) p_n(x) - C_n p_{n-1}(x) and the derivative rules sigma(x) p'_n(x) = alpha_n p_{n+1}(x) + beta_n p_n(x) + gamma_n p_{n-1}(x) and sigma(x) p'_n(x) = (alpha_n-tilde x + beta_n-tilde) p_n(x) + gamma_n-tilde p_{n-1}(x) respectively which are valid for the orthogonal ...
Koepf, Wolfram, Schmersau, Dieter
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On moments of classical orthogonal polynomials
Journal of Mathematical Analysis and Applications, 2015 Abstract In this work, using the inversion coefficients and some connection coefficients between some polynomial sets, we give explicit representations of the moments of all the orthogonal polynomials belonging to the Askey–Wilson scheme. Generating functions for some of these moments are also provided.
P. N. Sadjang +2 more
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Classical orthogonal polynomials: dependence of parameters
Journal of Computational and Applied Mathematics, 2000 The authors study connection problems between classical orthogonal polynomials and their derivatives with respect to (one of) their parameter(s). They use their so-called \texttt{Navima} algorithm to derive recurrence relations for the connection coefficients linking a family of classical orthogonal polynomials (like the Laguerre and Jacobi polynomials)
A. Zarzo +3 more
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On ( p , q ) $(p,q)$ -classical orthogonal polynomials and their characterization theorems
Advances in Difference Equations, 2017 In this paper, we introduce a general ( p , q ) $(p, q)$ -Sturm-Liouville difference equation whose solutions are ( p , q ) $(p, q)$ -analogues of classical orthogonal polynomials leading to Jacobi, Laguerre, and Hermite polynomials as ( p , q ) → ( 1 ...
M Masjed-Jamei +3 more
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Contemporary Mathematics, 2023 In this paper, new operational matrices (OMs) of ordinary and fractional derivatives (FDs) of a first finite class of classical orthogonal polynomials (FFCOP) are introduced.
H. M. Ahmed
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Elektronika ir Elektrotechnika, 2022 This paper presents one possible application of generalized quasi-orthogonal functional networks in the sensitivity analysis of complex dynamical systems.
Sasa S. Nikolic +6 more
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On the modifications of semi-classical orthogonal polynomials on nonuniform lattices
, 2017 S. Mboutngam +2 more
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On Certain Properties and Applications of the Perturbed Meixner–Pollaczek Weight
Mathematics, 2021 This paper deals with monic orthogonal polynomials orthogonal with a perturbation of classical Meixner–Pollaczek measure. These polynomials, called Perturbed Meixner–Pollaczek polynomials, are described by their weight function emanating from an ...
Abey S. Kelil +2 more
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The Stenger conjectures and the A-stability of collocation Runge-Kutta methods
Journal of Inequalities and Applications, 2023 Stenger conjectures are claims about the location of the eigenvalues of matrices whose elements are certain integrals involving basic Lagrange interpolating polynomials supported on the zeros of orthogonal polynomials. In this paper, we show the validity
Rachid Ait-Haddou, Hoda Alselami
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