Results 31 to 40 of about 79,087 (306)
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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On an system of “classical” polynomials of simultaneous orthogonality
Journal of Computational and Applied Mathematics, 1996 Let \(Q_{\overline n}(x)\), \(\overline n=(n_1,n_2)\), be the system of polynomials of simultaneous orthogonality [see \textit{E. M. Nikishin} and \textit{V. N. Sorokin}: ``Rational approximations and orthogonality'' (Russian orig. 1988; Zbl 0718.41002; Engl. transl. 1991; Zbl 0733.41001)] with \(\Delta_1=[a;0]\), \(\Delta_2=[0;1] (-1\leq a-1)\).
Kaliaguine, V., Ronveaux, André
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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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, 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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$q$-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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A Survey on q-Polynomials and their Orthogonality Properties [PDF]
, 2010 In this paper we study the orthogonality conditions satisfied by the classical q-orthogonal polynomials that are located at the top of the q-Hahn tableau (big q-jacobi polynomials (bqJ)) and the Nikiforov-Uvarov tableau (Askey-Wilson polynomials (AW ...
Alfaro +21 more
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Ain Shams Engineering Journal, 2018 The theme of this paper is to analyze and compare the pulse compression with classical orthogonal polynomials (Chebyshev, Laguerre, Legendre and Hermite polynomials) of different orders.
Ankur Thakur, Salman Raju Talluri
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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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Parameter Derivatives of the Jacobi Polynomials with Three Variables on the Simplex
MATEC Web of Conferences, 2016 In this paper, an attempt has been made to derive parameter derivatives of Jacobi polynomials with three variables on the simplex. They are obtained via parameter derivatives of the classical Jacobi polynomials Pn(α,β)(x) with respect to their parameters.
Aktaş Rabia
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A NEW CHARACTERIZATION OF 𝑞-CHEBYSHEV POLYNOMIALS OF THE SECOND KIND
Проблемы анализаIn this work, we introduce the notion of $\cal{U}_{(q, \mu)}$-classical orthogonal polynomials, where $\cal{U}_{(q, \mu)}$ is the degree raising shift operator defined by $\cal{U}_{(q, \mu)}$ $:= x(xH_q + q^{-1}I_{\cal{P}}) + \mu H_q$, where $\mu$ is a
S. Jbeli
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