New Approaches to the General Linearization Problem of Jacobi Polynomials Based on Moments and Connection Formulas

Abd-Elhameed, W. M.; Badah, Badah Mohamed

doi:10.3390/math9131573

Cited by 10 publications

(1 citation statement)

References 49 publications

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“…(see e.g. [1,2,8,13,24,32]). In particular, a general method, based on operational rules and generating functions, was developed for polynomial sets with equivalent lowering operators and with Boas-Buck generating functions [6,12,14].…”

Section: Introductionmentioning

confidence: 99%

Some Expansion Formulas for Brenke Polynomial Sets

Chaggara¹,

and²,

Romdhane³

2023

Preprint

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In this paper, we derive some explicit expansion formulas associated to Brenke polynomials using operational rules based on their corresponding generating functions. The obtained coefficients are expressed either in terms of finite double sums or finite sums or sometimes in closed hypergeometric terms. The derived results are applied to Generalized Gould-Hopper polynomials and Generalized Hermite polynomials introduced by Szegö and Chihara. Some well-known duplication and convolution formulas are deduced as particular cases.

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Section: Introductionmentioning

confidence: 99%

Some Expansion Formulas for Brenke Polynomial Sets

Chaggara¹,

and²,

Romdhane³

2023

Preprint

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New Formulas and Connections Involving Euler Polynomials

Abd-Elhameed

Amin

2022

Axioms

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The major goal of the current article is to create new formulas and connections between several well-known polynomials and the Euler polynomials. These formulas are developed using some of these polynomials’ well-known fundamental characteristics as well as those of the Euler polynomials. In terms of the Euler polynomials, new formulas for the derivatives of various symmetric and non-symmetric polynomials, including the well-known classical orthogonal polynomials, are given. This leads to the deduction of several new connection formulas between various polynomials and the Euler polynomials. As an important application, new closed forms for the definite integrals for the product of various symmetric and non-symmetric polynomials with the Euler polynomials are established based on the newly derived connection formulas.

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Novel Expressions for the Derivatives of Sixth Kind Chebyshev Polynomials: Spectral Solution of the Non-Linear One-Dimensional Burgers’ Equation

Abd-Elhameed¹

2021

Fractal Fract

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This paper is concerned with establishing novel expressions that express the derivative of any order of the orthogonal polynomials, namely, Chebyshev polynomials of the sixth kind in terms of Chebyshev polynomials themselves. We will prove that these expressions involve certain terminating hypergeometric functions of the type 4F3(1) that can be reduced in some specific cases. The derived expressions along with the linearization formula of Chebyshev polynomials of the sixth kind serve in obtaining a numerical solution of the non-linear one-dimensional Burgers’ equation based on the application of the spectral tau method. Convergence analysis of the proposed double shifted Chebyshev expansion of the sixth kind is investigated. Numerical results are displayed aiming to show the efficiency and applicability of the proposed algorithm.

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New Approaches to the General Linearization Problem of Jacobi Polynomials Based on Moments and Connection Formulas

Cited by 10 publications

References 49 publications

Some Expansion Formulas for Brenke Polynomial Sets

Some Expansion Formulas for Brenke Polynomial Sets

New Formulas and Connections Involving Euler Polynomials

Novel Expressions for the Derivatives of Sixth Kind Chebyshev Polynomials: Spectral Solution of the Non-Linear One-Dimensional Burgers’ Equation

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