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The Laguerre Constellation of Classical Orthogonal Polynomials
MathematicsA linear functional u is classical if there exist polynomials ϕ and ψ with degϕ≤2 and degψ=1 such that Dϕ(x)u=ψ(x)u, where D is a certain differential, or difference, operator. The polynomials orthogonal with respect to the linear functional u are called
Roberto S. Costas-Santos
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Classical Orthogonal Polynomials Revisited [PDF]
Results in Mathematics, 2023 AbstractThis 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, 2021 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 computation and a more efficient approach, such as the use of asymptotic expansions,is recommended. In
Amparo Gil, Javier Segura, Nico M. Temme
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d-Orthogonal Analogs of Classical Orthogonal Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2018 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. According to a famous theorem by Bochner they are the only systems on the real line with this property.
E. Horozov
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A ‘missing’ family of classical orthogonal polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2011 We study a family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type. These polynomials can be obtained from the little $q$-Jacobi polynomials in the limit $q=-1$.
Alexei Zhedanov, Luc Vinet
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On extreme zeros of classical orthogonal polynomials
Journal of Computational and Applied Mathematics, 2005 Let $x_1$ and $x_k$ be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree $k.$ We shall establish sharp inequalities of the form $x_1 B,$ which are uniform in all the parameters involved. Together with inequalities in the opposite direction, recently obtained by the author, this locates the extreme zeros of classical ...
Ilia Krasikov
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Results on the associated classical orthogonal polynomials
Journal of Computational and Applied Mathematics, 1995 AbstractLet {Pk(x)} be any system of the classical orthogonal polynomials, and let {Pk(x; c)} be the corresponding associated polynomials of order c (c ∈ N). Second-order recurrence relation (in k) is given for the connection coefficient an−1,k(c) in Pn−1(x;c)=σk=0n−1 an−1,k(c)Pk(x).
Stanisław Lewanowicz
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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 ...
Wolfram Koepf, Dieter Schmersau
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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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Characterizations of classical orthogonal polynomials on quadratic lattices [PDF]
, 2016 This paper is devoted to characterizations of classical orthogonal polynomials on quadratic lattices by using a matrix approach. In this form we recover the Hahn, Geronimus, Tricomi and Bochner type characterizations of classical orthogonal polynomials ...
Marlyse Njinkeu Sandjon +3 more
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