Results 41 to 50 of about 4,376 (199)

High-Order Numerical Solution of Second-Order One-Dimensional Hyperbolic Telegraph Equation Using a Shifted Gegenbauer Pseudospectral Method

, 2015
We present a high-order shifted Gegenbauer pseudospectral method (SGPM) to solve numerically the second-order one-dimensional hyperbolic telegraph equation provided with some initial and Dirichlet boundary conditions.
Elgindy, Kareem T.
core   +1 more source

Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds

Advances in Difference Equations, 2019
The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials.
Taekyun Kim, Dae San Kim, Dmitry V. Dolgy, Dojin Kim   +3 more
doaj   +1 more source

Criterion for polynomial solutions to a class of linear differential equation of second order [PDF]

, 2006
We consider the differential equations y''=\lambda_0(x)y'+s_0(x)y, where \lambda_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential equation, has a polynomial solution of degree n >0, then \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n ...
Al-Salam W A, Barakat T, Barakat T, Bayrak O, Chihara T S, Ciftci H, Ciftci H, Erdélyi A, Fernández M F, Grünbaum F A, Hakan Ciftci, Littlejohn L L, Nasser Saad, Richard L Hall, Saad N, Turbiner A   +15 more
core   +1 more source

Generalized Mixed Type Bernoulli-Gegenbauer Polynomials

Kragujevac Journal of Mathematics, 2023
The generalized mixed type Bernoulli-Gegenbauer polynomials of order α >−1/2 are special polynomials obtained by use of the generating function method. These polynomials represent an interesting mixture between two classes of special functions, namely generalized Bernoulli polynomials and Gegenbauer polynomials.
openaire   +3 more sources

Branching laws for Verma modules and applications in parabolic geometry. I [PDF]

, 2015
We initiate a new study of differential operators with symmetries and combine this with the study of branching laws for Verma modules of reductive Lie algebras.
Kobayashi, Toshiyuki, Somberg, Petr, Soucek, Vladimir, Ørsted, Bent   +3 more
core   +1 more source

Fractional Q$Q$‐curvature on the sphere and optimal partitions

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional Q$Q$‐curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of a symmetric minimal partition through a variational approach. A key ingredient in our analysis is a new
Héctor A. Chang‐Lara, Juan Carlos Fernández, Alberto Saldaña   +2 more
wiley   +1 more source

Radon Transform on spheres and generalized Bessel function associated with dihedral groups [PDF]

, 2012
Motivated by Dunkl operators theory, we consider a generating series involving a modified Bessel function and a Gegenbauer polynomial, that generalizes a known series already considered by L. Gegenbauer. We actually use inversion formulas for Fourier and
Demni, Nizar
core   +1 more source

Reconstruction Techniques for Inverse Sturm–Liouville Problems With Complex Coefficients

Mathematical Methods in the Applied Sciences, Volume 48, Issue 17, Page 15875-15889, 30 November 2025.
ABSTRACT A variety of inverse Sturm–Liouville problems is considered, including the two‐spectrum inverse problem, the problem of recovering the potential from the Weyl function, as well as the recovery from the spectral function. In all cases, the potential in the Sturm–Liouville equation is assumed to be complex valued.
Vladislav V. Kravchenko
wiley   +1 more source

New connection formulae for the q-orthogonal polynomials via a series expansion of the q-exponential

, 2006
Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and q-Gegenbauer ...
Aizawa N Chakrabarti R Naina Mohammed S S Segar J, Askey R, Erdélyi A, Gasper G, Kibler M, Odake S, R Chakrabarti, R Jagannathan, Raychev P P, S S Naina Mohammed   +9 more
core   +1 more source

On Generating Relations Involving Generalized Gegenbauer Polynomials [PDF]

Georgian Mathematical Journal, 2006
Abstract In this paper, generating relations involving generalized Gegenbauer polynomials are obtained by constructing a three-dimensional Lie algebra isomorphic to special linear algebra sl(2). Further, a number of new interesting relations involving various generalized polynomials are obtained as applications of these generating ...
Khan, Subuhi, Yasmin, Ghazala, Mittal, Archana   +2 more
openaire   +2 more sources