Results 21 to 30 of about 27,421 (244)
Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton q-Bessel function [PDF]
, 1995 Laurent polynomials related to the Hahn-Exton $q$-Bessel function, which are $q$-analogues of the Lommel polynomials, have been introduced by Koelink and Swarttouw.
Koelink, Erik, Van Assche, Walter
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Comparison between the Propagation Properties of Bessel–Gauss and Generalized Laguerre–Gauss Beams
Photonics, 2023 The connections between Laguerre–Gauss and Bessel–Gauss beams, and between Hermite–Gauss and cosine-Gauss beams are investigated. We review different asymptotic expressions for generalized Laguerre and Hermite polynomials of large radial/transverse order.
Colin J. R. Sheppard, Miguel A. Porras
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Useful Bases for Problems in Nuclear and Particle Physics [PDF]
, 1996 A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space and can be ...
Abramowitz +16 more
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A new class of orthogonal polynomials: The Bessel polynomials [PDF]
Transactions of the American Mathematical Society, 1949 The classical sets of orthogonal polynomials of Jacobi, Laguerre, and Hermite satisfy second order differential equations, and also have the property that their derivatives form orthogonal systems. There is a fourth class of polynomials with these two properties, and similar in other ways to the other three classes, which has hitherto been little ...
Orrin Frink, H. L. Krall
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Use of bessel polynomials for solving differential difference equations
Arab Journal of Basic and Applied Sciences, 2019 In this paper, the linear differential difference equation subject to the mixed conditions has been solved numerically using Bessel polynomials. The solution is obtained in terms of Bessel polynomials.
Zaffer Elahi +2 more
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Symmetry, 2023 Named essentially after their close relationship with the modified Bessel function Kν(z) of the second kind, which is known also as the Macdonald function (or, with a slightly different definition, the Basset function), the so-called Bessel polynomials yn(x) and the generalized Bessel polynomials yn(x;α,β) stemmed naturally in some systematic ...
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Ural Mathematical Journal, 2022 In this paper, we introduce the concept of the \(\mathbb{B}_{\alpha}\)-classical orthogonal polynomials, where \(\mathbb{B}_{\alpha}\) is the raising operator \(\mathbb{B}_{\alpha}:=x^2 \cdot {d}/{dx}+\big(2(\alpha-1)x+1\big)\mathbb{I}\), with nonzero ...
Baghdadi Aloui, Jihad Souissi
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Scaled Asymptotics For Some $q$-Series [PDF]
, 2007 In this work we investigate the asymptotics for Euler's $q$-Exponential $E_{q}(z)$, $q$-Gamma function $\Gamma_{q}(z)$, Ramanujan's function $A_{q}(z)$, Jackson's $q$-Bessel function $J_{\nu}^{(2)}$(z;q) of second kind, Stieltjes-Wigert orthogonal ...
Zhang, Ruiming
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On Lommel and Bessel polynomials [PDF]
Proceedings of the American Mathematical Society, 1954 hnk,(X) = Rn,(11X)2 we have a polynomial set that obeys 1n,,(X) = 2x(n + v1)In_1, (x) hn-2,,(X). It was noted by Hahn [5] that this is an orthogonal type recurrence relation. In this paper, we shall establish explicitly the orthogonality of the hn;,(x) and will present some properties of the Bessel polynomials yn(X), a polynomial set that is orthogonal
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Numerical study of sine-Gordon equations using Bessel collocation method [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2023 The nonlinear space time dynamics have been discussed in terms of a hyper-bolic equation known as a sine-Gordon equation. The proposed equation has been discretized using the Bessel collocation method with Bessel poly-nomials as base functions.
S. Arora, I. Bala
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