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Relevant bibliographies by topics / New formulae for Chebyshev polynomials

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Academic literature on the topic 'New formulae for Chebyshev polynomials'

Author: Grafiati

Published: 28 May 2022

Last updated: 29 May 2022

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Journal articles on the topic "New formulae for Chebyshev polynomials"

1

Abd-Elhameed, W. M. "New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems." Scientific World Journal 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/456501.

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This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of

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2

Abd-Elhameed, W. M., Y. H. Youssri, Nermine El-Sissi, and Mohammad Sadek. "New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials." Ramanujan Journal 42, no. 2 (2015): 347–61. http://dx.doi.org/10.1007/s11139-015-9712-x.

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3

Abd-Elhameed, Waleed Mohamed, and Seraj Omar Alkhamisi. "New Results of the Fifth-Kind Orthogonal Chebyshev Polynomials." Symmetry 13, no. 12 (2021): 2407. http://dx.doi.org/10.3390/sym13122407.

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The principal objective of this article is to develop new formulas of the so-called Chebyshev polynomials of the fifth-kind. Some fundamental properties and relations concerned with these polynomials are proposed. New moments formulas of these polynomials are obtained. Linearization formulas for these polynomials are derived using the moments formulas. Connection problems between the fifth-kind Chebyshev polynomials and some other orthogonal polynomials are explicitly solved. The linking coefficients are given in forms involving certain generalized hypergeometric functions. As special cases, t

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4

Abd-Elhameed, W. M., and Y. H. Youssri. "Sixth-Kind Chebyshev Spectral Approach for Solving Fractional Differential Equations." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 2 (2019): 191–203. http://dx.doi.org/10.1515/ijnsns-2018-0118.

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AbstractThe basic aim of this paper is to develop new numerical algorithms for solving some linear and nonlinear fractional-order differential equations. We have developed a new type of Chebyshev polynomials, namely, Chebyshev polynomials of sixth kind. This type of polynomials is a special class of symmetric orthogonal polynomials, involving four parameters that were constructed with the aid of the extended Sturm–Liouville theorem for symmetric functions. The proposed algorithms are basically built on reducing the fractional-order differential equations with their initial/boundary conditions

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5

Ercan, Elif, Mirac Cetin, and Naim Tuglu. "Incomplete q-Chebyshev polynomials." Filomat 32, no. 10 (2018): 3599–607. http://dx.doi.org/10.2298/fil1810599e.

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In this paper, we get the generating functions of the q-Chebyshev polynomials using ?z operator, which is ?z (f(z))= f(qz) for any given function f (z). Also considering explicit formulas of the q-Chebyshev polynomials, we give new generalizations of the q-Chebyshev polynomials called the incomplete q-Chebyshev polynomials of the first and second kind. We obtain recurrence relations and several properties of these polynomials. We show that there are connections between the incomplete q-Chebyshev polynomials and the some well-known polynomials.

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6

Hetmaniok, Edyta, Bożena Piątek, and Roman Wituła. "Binomials transformation formulae for scaled Fibonacci numbers." Open Mathematics 15, no. 1 (2017): 477–85. http://dx.doi.org/10.1515/math-2017-0047.

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Abstract The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.

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7

Hao, Gang Li, Wei Zao Wang, Xu Li Liang, and Hai Bo Wang. "The New Approximate Calculation Method for the First Order Reliability." Advanced Materials Research 694-697 (May 2013): 891–95. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.891.

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One new method is presented for computing engineering structure reliability by accelerating convergence based on the analysis of errors in the center point method and borrowing ideas form the merits of the other First-Order Second Moment (FOSM) methods. The accelerating convergence method is based on the first class Chebyshev polynomials. Firstly, the transformation relation of the first class Chebyshev polynomials and the power polynomials is given and expanded to vector formula. Secondly, the outstanding function approximate character of the first class Chebyshev polynomials can supply the h

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8

Doha, E. H., and W. M. Abd-Elhameed. "New linearization formulae for the products of Chebyshev polynomials of third and fourth kinds." Rocky Mountain Journal of Mathematics 46, no. 2 (2016): 443–60. http://dx.doi.org/10.1216/rmj-2016-46-2-443.

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9

Salih, Anam Alwan, and Suha SHIHAB. "New operational matrices approach for optimal control based on modified Chebyshev polynomials." Samarra Journal of Pure and Applied Science 2, no. 2 (2021): 68–78. http://dx.doi.org/10.54153/sjpas.2020.v2i2.115.

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    The purpose of this paper is to introduce interesting modified Chebyshev orthogonal polynomial. Then, their new operational matrices of derivative and integration or modified Chebyshev polynomials of the first kind are introduced with explicit formulas. A direct computational method for solving a special class of optimal control problem, named, the quadratic optimal control problem is proposed using the obtained operational matrices. More precisely, this method is based on a state parameterization scheme, which gives an accurate approximation of the exact solution b

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10

He, Tian-Xiao, and Peter J. S. Shiue. "On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–21. http://dx.doi.org/10.1155/2009/709386.

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Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a general method to construct identities of number or polynomial sequences defined by linear recurrence relations. The applications using the method to solve some algebraic and ordinary differential equations are presented.

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