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Construction of the Shifted Modified Gegenbauer Polynomials and Approximation [PDF]
Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.This article is concerned with deriving a new system of orthogonal polynomials, derived from the Gegenbauer polynomials, modified by affine transforms in variable, named shifted Gegenbauer polynomials. They appear as solutions of linear differential equation.
Abdelhamid Rehouma, Hossein Jafari
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Journal of Nigerian Society of Physical Sciences, 2023 In this paper, approximation of space fractional order diffusion equation are considered using compact finite difference technique to discretize the time derivative, which was then approximated via shifted Gegenbauer polynomials using zeros of (N - 1 ...
Kazeem Issa +3 more
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Sequences of Non-Gegenbauer-Humbert Polynomials Meet the Generalized Gegenbauer-Humbert Polynomials [PDF]
ISRN Algebra, 2011 Here, we present a connection between a sequence of polynomials generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials. Many new and known transfer formulas between non-Gegenbauer-Humbert polynomials and generalized Gegenbauer-Humbert polynomials are given.
Tian-Xiao He, Peter J.-S. Shiue
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An Operational Matrix Method Based on the Gegenbauer Polynomials for Solving a Class of Fractional Optimal Control Problems [PDF]
International Journal of Industrial Electronics, Control and Optimization, 2021 One of the most important classes of fractional calculus is the fractional optimal control problem (FOCP), which arises in engineering. This study presents a direct and efficient numerical method for solving a class of (FOCPs) in which the fractional ...
Farzaneh Soufivand +2 more
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Matrix-Valued Gegenbauer-Type Polynomials [PDF]
Constructive Approximation, 2017 Introducimos funciones de peso con valor de matriz de tamaño arbitrario, que son análogas a la función de peso para Gegenbauer o polinomios ultraesféricos para el parámetro $$\nu >0$$ . La descomposición LDU del peso se da explícitamente en términos de polinomios de Gegenbauer.
Erik Koelink +2 more
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New connection formulae for some q-orthogonal polynomials in q-Askey scheme [PDF]
, 2007 New nonlinear connection formulae of the q-orthogonal polynomials, such continuous q-Laguerre, continuous big q-Hermite, q-Meixner-Pollaczek and q-Gegenbauer polynomials, in terms of their respective classical analogues are obtained using a special ...
A Yanallah +7 more
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Some relations on Humbert matrix polynomials [PDF]
Mathematica Bohemica, 2016 The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix ...
Ayman Shehata
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Higher Derivatives of Airy Functions and of their Products [PDF]
, 2018 The problem of evaluation of higher derivatives of Airy functions in a closed form is investigated. General expressions for the polynomials which have arisen in explicit formulae for these derivatives are given in terms of particular values of Gegenbauer
Abramochkin, Eugeny G. +1 more
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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
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Runge-Kutta-Gegenbauer explicit methods for advection-diffusion problems [PDF]
, 2019 In this paper, Runge-Kutta-Gegenbauer (RKG) stability polynomials of arbitrarily high order of accuracy are introduced in closed form. The stability domain of RKG polynomials extends in the the real direction with the square of polynomial degree, and in ...
O'Sullivan, Stephen
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