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Classical Orthogonal Polynomials Revisited [PDF]
Results in Mathematics, 2023 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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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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On the functional equation for classical orthogonal polynomials on lattices [PDF]
Journal of Mathematical Analysis and Applications, 2021 Necessary and sufficient conditions for the regularity of solutions of the functional equation appearing in the theory of classical orthogonal polynomials on lattices are stated.
K. Castillo +2 more
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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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Some New Connection Relations Related to Classical Orthogonal Polynomials [PDF]
Journal of Mathematics, 2020 In this paper, we deal with a problem of positivity of linear functionals in the linear space ℙ of polynomials in one variable with complex coefficients.
Wathek Chammam, Wasim Ul-Haq
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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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Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials [PDF]
Mathematics of Computation, 2014 Barycentric interpolation is arguably the method of choice for numerical polynomial interpolation. In this paper we show that barycentric weights for the roots or extrema of classical families of orthogonal polynomials are expressible explicitly in terms
Haiyong Wang +2 more
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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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Point vortices and classical orthogonal polynomials [PDF]
, 2012 Stationary equilibria of point vortices in the plane and on the cylinder in the presence of a background flow are studied. Vortex systems with an arbitrary choice of circulations are considered.
Maria V. Demina, Nikolay A. Kudryashov
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