Results 51 to 60 of about 411,141 (342)
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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q-Hermite Polynomials and Classical Orthogonal Polynomials [PDF]
Canadian Journal of Mathematics, 1996 AbstractWe use generating functions to express orthogonality relations in the form of q-beta. integrals. The integrand of such a q-beta. integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials ...
Christian Berg, Mourad E. H. Ismail
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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
semanticscholar +1 more source
, 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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The relation of the d-orthogonal polynomials to the Appell polynomials [PDF]
, 1996 We are dealing with the concept of d-dimensional orthogonal (abbreviated d-orthogonal) polynomials, that is to say polynomials verifying one standard recurrence relation of order d + 1.
Douak, Khalfa
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On a new characterization of the classical orthogonal polynomials
Journal of Approximation Theory, 1992 AbstractIn this paper we give a new characterization of the classical orthogonal polynomials (Jacobi, Laguerre, and Hermite polynomials) by a special property of the sequences in their recurrence formula. The results also allow an easy derivation of the asymptotic distribution of the zeros of the classical orthogonal polynomials.
Holger Dette, W. J. Studden
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$q$-Classical orthogonal polynomials: A general difference calculus approach
, 2009 It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator.
A.F. Nikiforov +26 more
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Generalization of matching extensions in graphs—combinatorial interpretation of orthogonal and q-orthogonal polynomials [PDF]
, 2005 In this paper, we present generalization of matching extensions in graphs and we derive combinatorial interpretation of wide classes of orthogonal and q-orthogonal polynomials. Specifically, we assign general weights to complete graphs, cycles and chains
Kyriakoussis, A., Vamvakari, M.G.
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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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Curvilinearity and Orthogonality [PDF]
arXiv, 2022 We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal ...
arxiv