Results 71 to 80 of about 320 (175)

On an Energy-Dependent Quantum System with Solutions in Terms of a Class of Hypergeometric Para-Orthogonal Polynomials on the Unit Circle

Mathematics, 2020
We study an energy-dependent potential related to the Rosen–Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrödinger operator in terms of a class of functions associated to a family of hypergeometric para ...
Jorge A. Borrego-Morell, Cleonice F. Bracciali, Alagacone Sri Ranga   +2 more
doaj   +1 more source

Matrix-valued Gegenbauer polynomials

, 2014
25 pages, accompanying Maple worksheet available at http://www.math.ru.nl/~koelink/publist-ro.html. Proofs have been simplified by exploiting shift operators extensively. The proofs of the symmetry of some matrix-valued differential operators have been simplified using the LDU-decomposition of the weight. The proof of the matrix-valued Pearson equation
Koelink, Erik, Rios, Ana M. de los, Roman, Pablo   +2 more
openaire   +2 more sources

Fourier–Gegenbauer Integral Galerkin Method for Solving the Advection–Diffusion Equation with Periodic Boundary Conditions

Computation
This study presents the Fourier–Gegenbauer integral Galerkin (FGIG) method, a new numerical framework that uniquely integrates Fourier series and Gegenbauer polynomials to solve the one-dimensional advection–diffusion (AD) equation with spatially ...
Kareem T. Elgindy
doaj   +1 more source

A numerical technique for solving multi-dimensional fractional optimal control problems

Journal of Taibah University for Science, 2018
In this article, we use the operation matrix (OM) of Riemann–Liouville fractional integral of the shifted Gegenbauer polynomials with the Lagrange multiplier method to provide efficient numerical solutions to the multi-dimensional fractional optimal ...
Hoda F. Ahmed
doaj   +1 more source

The Orthogonal Riesz Fractional Derivative

Axioms
The aim of this paper is to extend the concept of the orthogonal derivative to provide a new integral representation of the fractional Riesz derivative. Specifically, we investigate the orthogonal derivative associated with Gegenbauer polynomials Cn(ν)(x)
Fethi Bouzeffour
doaj   +1 more source

Bounds for the Second Hankel Determinant of a General Subclass of Bi-Univalent Functions [PDF]

International Journal of Mathematical, Engineering and Management Sciences
The Hankel determinant, which plays a significant role in the theory of univalent functions, is investigated here in the context of bi-univalent analytic functions.
Mohamed Illafe, Maisarah Haji Mohd, Feras Yousef, Shamani Supramaniam   +3 more
doaj   +1 more source

Oblique Water Wave Diffraction by a Step

International Journal of Applied Mechanics and Engineering, 2017
This paper is concerned with the problem of diffraction of an obliquely incident surface water wave train on an obstacle in the form of a finite step.
P. Dolai
doaj   +1 more source

Generalized Gegenbauer orthogonal polynomials

Journal of Computational and Applied Mathematics, 2001
The aim of the author is to give a characterization of the so-called generalized Gegenbauer polynomials. He first shows the link between this functions and the classical Jacobi polynomials. Then he establishes both a differential-difference and a second order differential equation satisfied by these generalized polynomials.
openaire   +2 more sources

On the derivatives of generalized Gegenbauer polynomials

, 2002
3 pages, no figures; submitted to Theor.
García Fuertes, Wifredo, Perelomov, Askold M.   +1 more
openaire   +3 more sources

Discrete-Time Filter Synthesis using Product of Gegenbauer Polynomials [PDF]

Radioengineering, 2016
A new approximation to design continuoustime and discrete-time low-pass filters, presented in this paper, based on the product of Gegenbauer polynomials, provides the ability of more flexible adjustment of passband and stopband responses.
N. Stojanovic, N. Stamenkovic, I. Krstic
doaj