Results 21 to 30 of about 320 (175)

Some results for sums of products of Chebyshev and Legendre polynomials

Advances in Difference Equations, 2019
In this paper, we perform a further investigation of the Gegenbauer polynomials, the Chebyshev polynomials of the first and second kinds and the Legendre polynomials.
Yuan He
doaj   +1 more source

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

Fourier Series of Gegenbauer-Sobolev Polynomials [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2018
We study the partial sum operator for a Sobolev-type inner product related to the classical Gegenbauer polynomials. A complete characterization of the partial sum operator in an appropriate Sobolev space is given. Moreover, we analyze the convergence of the partial sum operators.
Ciaurri, Ó., Mínguez, J.
openaire   +6 more sources

Some identities involving generalized Gegenbauer polynomials

Advances in Difference Equations, 2017
In this paper, we investigate some interesting identities on the Bernoulli, Euler, Hermite and generalized Gegenbauer polynomials arising from the orthogonality of generalized Gegenbauer polynomials in the generalized inner product 〈 p 1 ( x ) , p 2 ( x )
Zhaoxiang Zhang
doaj   +1 more source

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

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

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

Gegenbauer polynomials and the Fueter theorem [PDF]

Complex Variables and Elliptic Equations, 2013
The Fueter theorem states that regular (resp. monogenic) functions in quaternionic (resp. Clifford) analysis can be constructed from holomorphic functions in the complex plane, hereby using a combination of a formal substitution and the action of an appropriate power of the Laplace operator.
Eelbode, David, Soucek, Vladimir, Van Lancker, Peter   +2 more
openaire   +3 more sources

A derivative-based extension of Gegenbauer polynomials in two variables

Nuclear Physics B
In this paper, a new class of two-variable Gegenbauer-type polynomials is introduced via a derivative-based construction. The definition incorporates an additional variable through finite sums involving higher-order derivatives of classical Gegenbauer ...
Özge Ada, Esra Erkuş-Duman
doaj   +1 more source

The Spectral Connection Matrix for Any Change of Basis within the Classical Real Orthogonal Polynomials

Mathematics, 2015
The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials.
Tom Bella, Jenna Reis
doaj   +1 more source