Results 21 to 30 of about 5,734 (154)

Representing by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials

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, Dae San Kim, Lee-Chae Jang, D. V. Dolgy   +3 more
doaj   +1 more source

Matrix Gegenbauer Polynomials: the $2\times 2$ Fundamental Cases [PDF]

, 2015
In this paper, we exhibit explicitly a sequence of $2\times2$ matrix valued orthogonal polynomials with respect to a weight $W_{p,n}$, for any pair of real numbers $p$ and $n$ such that ...
Pacharoni, Inés, Zurrián, Ignacio
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Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials

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, Dae San Kim, Jongkyum Kwon, Dmitry V. Dolgy   +3 more
doaj   +1 more source

Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems [PDF]

, 2013
We develop complex Jacobi, Gegenbauer and Chebyshev polynomial expansions for the kernels associated with power-law fundamental solutions of the polyharmonic equation on d-dimensional Euclidean space.
Cohl, Howard S.
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Quasilinearization method to solve several classes of nonlinear Lane-Emden equations by Gegenbauer polynomials [PDF]

Iranian Journal of Numerical Analysis and Optimization
This paper presents a comprehensive numerical approach for solving various types of singular nonlinear Lane-Emden equations. The proposed method begins by applying the Quasilinearization Method (QLM), to transform the nonlinear differential equation into
Fateme Sheikhi, Bahman Ghazanfari
doaj   +1 more source

Conformal string operators and evolution of skewed parton distributions [PDF]

, 1999
We have investigated skewed parton distributions in coordinate space. We found that their evolution can be described in a simple manner in terms of non-local, conformal operators introduced by Balitsky and Braun.
Balitskii, Balitsky, Belitsky, Belitsky, Belitsky, Blümlein, Braun, Brodsky, Brodsky, Carlson, Chase, Chase, Collins, Crittenden, Del Duca, Efremov, Efremov, Efremov, Erdelyi, Frankfurt, Frankfurt, Golec-Biernat, Gradshteyn, Gribov, Guichon, Hoodbhoy, Hoyer, Ioffe, Ioffe, Ioffe, Ji, Ji, Ji, Kantorovich, L. Mankiewicz, Makeenko, Mankiewicz, Mankiewicz, Mankiewicz, Mankiewicz, N. Kivel, Ohrndorf, Pestieau, Radyushkin, Radyushkin, Ryskin, van der Steenhoven, Vanderhaeghen, Vänttinen   +48 more
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On the $$L^2$$-norm of Gegenbauer polynomials [PDF]

Mathematical Sciences, 2021
AbstractGegenbauer, also known as ultra-spherical, polynomials appear often in numerical analysis or interpolation. In the present text we find a recursive formula for and compute the asymptotic behavior of their $$L^2$$ L 2 -norm.
openaire   +3 more sources

The finite Fourier transform of classical polynomials [PDF]

, 2014
The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain.
Dixit, Atul, Jiu, Lin, Moll, Victor H., Vignat, Christophe   +3 more
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Representing by Orthogonal Polynomials for Sums of Finite Products of Fubini Polynomials

Mathematics, 2019
In the classical connection problem, it is dealt with determining the coefficients in the expansion of the product of two polynomials with regard to any given sequence of polynomials.
Dae San Kim, Dmitry V. Dolgy, Dojin Kim, Taekyun Kim   +3 more
doaj   +1 more source

Algebraic Generating Functions for Gegenbauer Polynomials

, 2017
It is shown that several of Brafman's generating functions for the Gegenbauer polynomials are algebraic functions of their arguments, if the Gegenbauer parameter differs from an integer by one-fourth or one-sixth.
Maier, Robert S.
core   +1 more source