Results 71 to 80 of about 411,141 (342)
On the $D_ω$-classical orthogonal polynomials [PDF]
arXiv, 2023 We wish to investigate the $D_{\omega}$-classical orthogonal polynomials, where $D_{\omega}$ is a special case of the Hahn operator. For this purpose, we consider the problem of finding all sequences of orthogonal polynomials such that their $D_{\omega}$-derivatives are also orthogonal polynomials. To solve this problem we adopt a different approach to
arxiv
Classical discrete symplectic ensembles on the linear and exponential lattice: skew orthogonal polynomials and correlation functions [PDF]
Transactions of the American Mathematical Society, 2019 The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalized to discrete settings involving either a linear or an exponential lattice. The corresponding correlation functions can be expressed in terms of
P. Forrester, Shi-Hao Li
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Duality for classical orthogonal polynomials
Journal of Computational and Applied Mathematics, 2005 AbstractSome aspects of duality for the classical orthogonal polynomials are explained. Duality deals with the similarity of these functions as functions of the orthogonality variable and of the degree of the polynomials.
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New characterizations of classical orthogonal polynomials
Indagationes Mathematicae, 1996 AbstractClassical orthogonal polynomials of Jacobi, Laguerre, Hermite, and Bessel are characterized as the only orthogonal polynomials (up to a linear change of variable) such that 1.(i) (Bochner) they satisfy a second order differential equation of the form l2(x)y″(x) + l1(x)y′(x) = λny(x); and2.(ii) (Hahn) their derivatives of any fixed order are ...
Kil Hyun Kwon +8 more
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Advanced Materials Technologies, EarlyView.A novel approach enables facile and reproducible fabrication of gold nanoparticle arrays with tunable near‐infrared plasmonic properties and enhanced sensing accuracy. Using advanced lithography and ion milling, combined with innovative surface chemistry, the approach minimizes ohmic losses and non‐specific sorption, improving biomolecular detection ...
Dario Cattozzo Mor +12 more
wiley +1 more source
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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Some New Connection Relations Related to Classical Orthogonal Polynomials
Journal of Mathematics, 2020 In this paper, we deal with a problem of positivity of linear functionals in the linear space ℙ of polynomials in one variable with complex coefficients.
Wathek Chammam, Wasim Ul-Haq
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مجلة العلوم البحتة والتطبيقية, 2020 The connection between different classes of special functions is a very important aspect in establishing new properties of the related classical functions that is they can inherit the properties of each other. Here we show how the Hermite polynomials are
Haniyah Saed Ben Hamdin
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AIMS Mathematics, 2023 In this study, we develop various features in special polynomials using the principle of monomiality, operational formalism, and other qualities. By utilizing the monomiality principle, new outcomes can be achieved while staying consistent with past ...
Mohra Zayed, Shahid Wani
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Three-fold symmetric Hahn-classical multiple orthogonal polynomials [PDF]
Analysis and Applications, 2018 We characterize all the multiple orthogonal three-fold symmetric polynomial sequences whose sequence of derivatives is also multiple orthogonal. Such a property is commonly called the Hahn property and it is an extension of the concept of classical ...
A. Loureiro, W. Assche
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