Results 21 to 30 of about 28,297 (240)
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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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 ...
Krall, H. L., Frink, Orrin
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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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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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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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Appell-Type Functions and Chebyshev Polynomials
Mathematics, 2019 In a recent article we noted that the first and second kind Cebyshev polynomials can be used to separate the real from the imaginary part of the Appell polynomials. The purpose of this article is to show that the same classic polynomials can also be used
Pierpaolo Natalini, Paolo Emilio Ricci
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Integral representations for the product of certain polynomials of two variables
Ain Shams Engineering Journal, 2013 The main object of this paper is to investigate several integral representations for the product of two polynomials of two variables, e.g. Laguerre, Jacobi, Generalized Bessel, Generalized Rice, Krawtchouk, Meixner, Gottlieb and Poisson–Charlier ...
Mumtaz Ahmad Khan +2 more
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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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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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Polynomial approximations to Bessel functions [PDF]
IEEE Transactions on Antennas and Propagation, 2003 A polynomial approximation to Bessel functions that arises from an electromagnetic scattering problem is examined. The approximation is extended to Bessel functions of any integer order, and the relationship to the Taylor series is derived. Numerical calculations show that the polynomial approximation and the Taylor series truncated to the same order ...
Millane, R.P., Eads, J.L.
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