Results 81 to 90 of about 351,291 (192)
Equilibria of `Discrete' Integrable Systems and Deformations of Classical Orthogonal Polynomials
, 2004 The Ruijsenaars-Schneider systems are `discrete' version of the Calogero-Moser (C-M) systems in the sense that the momentum operator p appears in the Hamiltonians as a polynomial in e^{\pm\beta' p} (\beta' is a deformation parameter) instead of an ...
Andrews G E +29 more
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Проблемы анализа, 2019 In this paper, we introduce the notion of Oε-classical orthogonal polynomials, where Oε := I + εD (ε 6= 0). It is shown that the scaled Laguerre polynomial sequence {a −nL (α) n (ax)}n>0, where a = −ε −1 , is actually the only Oε-classical ...
B. Aloui, L. Kheriji
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Weak convergence of orthogonal polynomials [PDF]
arXiv, 1994 The weak convergence of orthogonal polynomials is given under conditions on the asymptotic behaviour of the coefficients in the three-term recurrence relation. The results generalize known results and are applied to several systems of orthogonal polynomials, including orthogonal polynomials on a finite set of points.
arxiv
Mathematics, 2015 The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials.
Tom Bella, Jenna Reis
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Alternative Jacobi Polynomials and Orthogonal Exponentials [PDF]
arXiv, 2011 Sequences of orthogonal polynomials that are alternative to the Jacobi polynomials on the interval $[0,1]$ are defined and their properties are established. An $(\alpha,\beta)$-parameterized system of orthogonal polynomials of the exponential function on the semi-axis $[0,\infty)$ is presented.
arxiv
The Associated Classical Orthogonal Polynomials [PDF]
, 2001 The associated orthogonal polynomials p n (x;c) are defined by the 3-term recurrence relation with coefficients A n , B n , C n for p n (x) with c = 0, replaced by A n+c, B n+cand C n+c, c being the association parameter. Starting with examples where such polynomials occur in a natural way some of the well-known theories of how to determine their ...
openaire +2 more sources
, 2012 This thesis will show work on Orthogonal Polynomials. In mathematics, the type of polynomials that are orthogonal to each other under inner product are called orthogonal polynomials.
Antashyan, George Gevork
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Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices
, 2005 We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number.
A. F. Nikiforov +15 more
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A matrix Rodrigues formula for classical orthogonal polynomials in two variables [PDF]
arXiv, 2006 Classical orthogonal polynomials in one variable can be characterized as the only orthogonal polynomials satisfying a Rodrigues formula. In this paper, using the second kind Kronecker power of a matrix, a Rodrigues formula is introduced for classical orthogonal polynomials in two variables.
arxiv
A Characterization of "Classical" d-Orthogonal Polynomials
Journal of Approximation Theory, 1995 AbstractWe give a characterization of "classical" d-orthogonal polynomials through a vectorial functional equation. A sequence of monic polynomials {Bn}n ≥ 0 is called d-simultaneous orthogonal or simply d-orthogonal if it fulfils the following d + 1-st order recurrence relation: [formula] with the initial conditions [formula] Denoting by {Ln}n ≥ 0 the
Khalfa Douak, Pascal Maroni
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