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Asymptotic computation of classical orthogonal polynomials [PDF]
Orthogonal Polynomials: Current Trends and Applications, 2020 The classical orthogonal polynomials (Hermite, Laguerre and Jacobi) are involved in a vast number of applications in physics and engineering. When large degrees $n$ are needed, the use of recursion to compute the polynomials is not a good strategy for ...
A. Gil, J. Segura, N. M. Temme
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Classical Orthogonal Polynomials Revisited [PDF]
Results in Mathematics, 2021 This manuscript contains a small portion of the algebraic theory of orthogonal polynomials developed by Maroni and their applicability to the study and characterization of the classical families, namely Hermite, Laguerre, Jacobi, and Bessel polynomials ...
K. Castillo, J. Petronilho
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On Semi-Classical Orthogonal Polynomials Associated with a Modified Sextic Freud-Type Weight [PDF]
Mathematics, 2020 Polynomials that are orthogonal with respect to a perturbation of the Freud weight function by some parameter, known to be modified Freudian orthogonal polynomials, are considered. In this contribution, we investigate certain properties of semi-classical
Abey Sherif Kelil, Appanah Rao Appadu
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d-Orthogonal Analogs of Classical Orthogonal Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2016 Classical orthogonal polynomial systems of Jacobi, Hermite and Laguerre have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator.
E. Horozov
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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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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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Dunkl-supersymmetric orthogonal functions associated with classical orthogonal polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2019 We consider the eigenvalue problem associated with the Dunkl-type differential operator (in which the reflection operator R is involved) in the context of supersymmetric quantum mechanical models. By solving this eigenvalue problem with the help of known
Yu Luo +3 more
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Ain Shams Engineering Journal, 2018 The theme of this paper is to analyze and compare the pulse compression with classical orthogonal polynomials (Chebyshev, Laguerre, Legendre and Hermite polynomials) of different orders.
Ankur Thakur, Salman Raju Talluri
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Classical 2-orthogonal polynomials and differential equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 We construct the linear differential equations of third order satisfied by the classical 2‐orthogonal polynomials. We show that these differential equations have the following form: , where the coefficients are polynomials whose degrees are, respectively, less than or equal to 4, 3, 2, and 1. We also show that the coefficient R4,n(x) can be written as
Boukhemis Ammar, Zerouki Ebtissem
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Classical Sobolev Orthogonal Polynomials: Eigenvalue Problem [PDF]
Results in Mathematics, 2019 We consider the discrete Sobolev inner product $$(f,g)_S=\int f(x)g(x)d +Mf^{(j)}(c)g^{(j)}(c), \quad j\in \mathbb{N}\cup\{0\}, \quad c\in\mathbb{R}, \quad M>0, $$ where $ $ is a classical continuous measure with support on the real line (Jacobi, Laguerre or Hermite).
Juan F. Mañas-Mañas +1 more
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