Results 71 to 80 of about 2,335 (226)
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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Monolithic Newton‐Multigrid Finite Element Methods for the Simulation of Thixoviscoplastic Flows
International Journal for Numerical Methods in Fluids, Volume 97, Issue 4, Page 565-604, April 2025.ABSTRACT In this paper, we shall be concerned with the development, application, and numerical analysis of the monolithic Newton‐Multigrid finite element method (FEM) to simulate thixoviscoplastic (TVP) flows. We demonstrate the importance of robustness and efficiency of Newton‐Multigrid FEM solver for obtaining accurate solutions.
Naheed Begum +2 more
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A new family of orthogonal polynomials in three variables
Journal of Inequalities and Applications, 2020 In this paper we introduce a six-parameter generalization of the four-parameter three-variable polynomials on the simplex and we investigate the properties of these polynomials.
Rabia Aktaş +2 more
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Multi‐Slit Diffraction in Scaled Space‐Time
Natural Sciences, Volume 5, Issue 1-2, April 2025.A space‐time scaling is used to transform quantum wave packets describing free particle motion to packets moving in an effective harmonic oscillator potential that confines and directs the wave fronts along the classical phase space of the oscillator. The transformation is applied to multi‐slit diffraction and shown to characterize diffraction features
James M. Feagin
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Fortschritte der Physik, Volume 73, Issue 4, April 2025.Abstract The Kerr metric is a vacuum solution of the Einstein equations outside of a rotating black hole (BH), but what interior matter is actually rotating and sourcing the Kerr geometry? Here, a rotating exotic matter is described, which can source the Kerr geometry for the entire acceptable range of its spin parameter and be shown to saturate the ...
Ram Brustein, A.J.M. Medved
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Advances in Difference Equations, 2019 In this paper, we investigate sums of finite products of Chebyshev polynomials of the first kind and those of Lucas polynomials. We express each of them as linear combinations of Hermite, extended Laguerre, Legendre, Gegenbauer, and Jacobi polynomials ...
Taekyun Kim +3 more
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Some generalized Jacobi polynomials
Computers & Mathematics with Applications, 2003 AbstractWe give explicitly the recurrence coefficients in the three term recurrence relation of some generalized Jacobi polynomials defined by the positive weight ϱ(α,α + p;x,μ) = ‖−μ(1−x2)α(1−x)p on [−1, +1]. The case p = 0 can be found in Chihara's book. The case p = 1 is treated by the first author, and we consider here the cases p = 2,3,4.
J. Alaya, A. Ronveaux, M. J. Atia
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Studies in Applied Mathematics, Volume 154, Issue 4, April 2025.ABSTRACT In this paper, we compute the small and large x$x$ asymptotics of the special function solutions of the Painlevé‐III equation in the complex plane. We use the representation in terms of Toeplitz determinants of Bessel functions obtained by Masuda. Toeplitz determinants are rewritten as multiple contour integrals using Andrèief's identity.
Hao Pan, Andrei Prokhorov
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Riemann–Liouville Operator in Weighted Lp Spaces via the Jacobi Series Expansion
Axioms, 2019 In this paper, we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann−Liouville fractional integral and derivative operators on a compact of the real axis.
Maksim V. Kukushkin
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On the Extreme Zeros of Jacobi Polynomials
, 2023 By applying the Euler--Rayleigh methods to a specific representation of the Jacobi polynomials as hypergeometric functions, we obtain new bounds for their largest zeros. In particular, we derive upper and lower bound for $1-x_{nn}^2( )$, with $x_{nn}( )$ being the largest zero of the $n$-th ultraspherical polynomial $P_n^{( )}$.
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