Results 61 to 70 of about 984,401 (366)
Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials
Advances in Mathematical Physics, 2018 Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived.
Oksana Bihun, Clark Mourning
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On Certain Properties and Applications of the Perturbed Meixner–Pollaczek Weight
Mathematics, 2021 This paper deals with monic orthogonal polynomials orthogonal with a perturbation of classical Meixner–Pollaczek measure. These polynomials, called Perturbed Meixner–Pollaczek polynomials, are described by their weight function emanating from an ...
Abey S. Kelil +2 more
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, 2005 The equilibrium positions of the multi-particle classical Calogero-Sutherland-Moser (CSM) systems with rational/trigonometric potentials associated with the classical root systems are described by the classical orthogonal polynomials; the Hermite ...
Odake, S., Sasaki, R.
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A Number of Quasi-Exactly Solvable N-body Problems [PDF]
, 1998 We present several examples of quasi-exactly solvable $N$-body problems in one, two and higher dimensions. We study various aspects of these problems in some detail. In particular, we show that in some of these examples the corresponding polynomials form
Avinash Khare +2 more
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Generating new classes of orthogonal polynomials
International Journal of Mathematics and Mathematical Sciences, 1996 Given a sequence of monic orthogonal polynomials (MOPS), {Pn}, with respect to a quasi-definite linear functional u, we find necessary and sufficient conditions on the parameters an and bn for the sequence Pn(x)+anPn−1(x)+bnPn−2(x), n≥1P0(x)=1,P−1(x ...
Amílcar Branquinho +1 more
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Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems
, 2013 We study the Plancherel--Rotach asymptotics of four families of orthogonal polynomials, the Chen--Ismail polynomials, the Berg-Letessier-Valent polynomials, the Conrad--Flajolet polynomials I and II.
Dai, Dan +2 more
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Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials [PDF]
Mathematics of Computation, 2012 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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Computational Modeling of Reticular Materials: The Past, the Present, and the Future
Advanced Materials, EarlyView.Reticular materials are advanced materials with applications in emerging technologies. A thorough understanding of material properties at operating conditions is critical to accelerate the deployment at an industrial scale. Herein, the status of computational modeling of reticular materials is reviewed, supplemented with topical examples highlighting ...
Wim Temmerman +3 more
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Orthogonal Polynomials in Mathematical Physics
, 2017 This is a review of ($q$-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot theory.
Chan, Chuan-Tsung +3 more
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Anti-isospectral Transformations, Orthogonal Polynomials and Quasi-Exactly Solvable Problems [PDF]
, 1997 We consider the double sinh-Gordon potential which is a quasi-exactly solvable problem and show that in this case one has two sets of Bender-Dunne orthogonal polynomials .
Avinash Khare +2 more
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