Results 41 to 50 of about 57,584 (243)
Determinant inequalities for sieved ultraspherical polynomials
International Journal of Mathematics and Mathematical Sciences, 2001 Paul Turan first observed that the Legendre polynomials satisfy the inequality Pn2(x)−Pn−1(x)Pn(x)>0 ...
J. Bustoz, I. S. Pyung
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Discrete semi-classical orthogonal polynomials of class one on quadratic lattices
Journal of difference equations and applications (Print), 2018 We study orthogonal polynomials on quadratic lattices with respect to Stieltjes functions, S, that satisfy a difference equation where A is a polynomial of degree less or equal than 3 and C is a polynomial of degree greater or equal than 1 and less or ...
G. Filipuk, M. N. Rebocho
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On a new characterization of the classical orthogonal polynomials
Journal of Approximation Theory, 1992 The truncated and reversed measure \(\mu_ n^ R\) is defined on \([0;1]\), \([0;\infty)\), or \((-\infty;\infty)\) as a measure corresponding to \((2n- 1)\)-th approximant of a \(g\)-fraction, \(n\)-th approximant of a modified \(S\)-fraction, or \(n\)-th approximant of a \(J\)-fraction correspondingly [see \textit{W. B. Jones} and \textit{W.J.
Holger Dette, W. J. Studden
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New Formulas and Connections Involving Euler Polynomials
Axioms, 2022 The major goal of the current article is to create new formulas and connections between several well-known polynomials and the Euler polynomials. These formulas are developed using some of these polynomials’ well-known fundamental characteristics as well
Waleed Mohamed Abd-Elhameed +1 more
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CHARACTERIZATION OF POLYNOMIALS VIA A RAISING OPERATOR
Проблемы анализа, 2023 This paper investigates a first-order linear differential operator 𝒥𝜉, where 𝜉 = (𝜉1, 𝜉2)\in (C^2\(0,0), and 𝐷 := 𝑑/𝑑𝑥. The operator is defined as 𝒥𝜉 := 𝑥(𝑥𝐷+ I) + 𝜉1 I + 𝜉2𝐷, with I representing the identity on the space of polynomials with complex ...
Jihad Souissi
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Duality for classical orthogonal polynomials
Journal of Computational and Applied Mathematics, 2005 Some aspects of duality for the classical orthogonal polynomials named after Laguerre and Jacobi are explained. The Laguerre polynomials form a limit case of the discrete Meixner polynomials. A certain integral identity involving Laguerre polynomials can be obtained as a limiting case of an identity involving Meixner polynomials.
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New characterizations of classical orthogonal polynomials
Indagationes Mathematicae, 1996 The authors reconsider the classical orthogonal polynomials (i.e., Jacobi, Laguerre, Hermite and Bessel polynomials) and give some new characterizations of them. The results are expressed in the form of two theorems which claim that some statements are equivalent to each other.
Kil Hyun Kwon +8 more
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Mathematics, 2018 This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials.
Taekyun Kim +3 more
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Perturbations around the zeros of classical orthogonal polynomials [PDF]
, 2014 Starting from degree N solutions of a time dependent Schrodinger-like equation for classical orthogonal polynomials, a linear matrix equation describing perturbations around the N zeros of the polynomial is derived.
R. Sasaki
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Extensions of discrete classical orthogonal polynomials beyond the orthogonality
Journal of Computational and Applied Mathematics, 2009 It is well known that the family of Hahn polynomials $\{h_n^{ , }(x;N)\}_{n\ge 0}$ is orthogonal with respect to a certain weight function up to $N$. In this paper we present a factorization for Hahn polynomials for a degree higher than $N$ and we prove that these polynomials can be characterized by a $ $-Sobolev orthogonality.
Costas-Santos, Roberto S. +1 more
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