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Algorithms for classical orthogonal polynomials [PDF]
, 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-
Koepf, Wolfram, Schmersau, Dieter
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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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Results on the associated classical orthogonal polynomials
Journal of Computational and Applied Mathematics, 1995 Let \(\{P_k (x) \}^\infty_{k=0}\) denote a system of classical orthogonal polynomials, i.e., a system of Jacobi, Laguerre, or Hermite polynomials, and let \(\{P_k (x; c) \}^\infty_{k=0}\) be the corresponding associated polynomials of order \(c\in \mathbb{N}\), i.e., if the polynomials \(P_k (x)\), \(k=0, 1, \dots\), satisfy the 3-term recurrence ...
Stanisław Lewanowicz
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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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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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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 ...
Alexander Ivanovich Aptekarev +2 more
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Zero distribution of sequences of classical orthogonal polynomials [PDF]
Abstract and Applied Analysis, 2003 We obtain the zero distribution of sequences of classical orthogonal polynomials associated with Jacobi, Laguerre, and Hermite weights. We show that the limit measure is the extremal measure associated with the corresponding weight.
Plamen Simeonov
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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. Ronveaux +3 more
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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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