An Extension of the Chebyshev Polynomials

Tatarczak, Anna

doi:10.1007/s11785-015-0503-6

Cited by 4 publications

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“…The celebrated Chebyshev polynomials have a wide range of applications in many fields such as numerical analysis, differential equations, approximation theory, and number theory (see, e.g., [2,9,6]). Some extensions and recent developments of the Chebyshev polynomials can be found, e.g., in [17,8,5,12,11,7,10]. As is well known, the Chebyshev polynomials of the first kind are defined by the recurrence relation T 0 (t) = 1, T 1 (t) = t, T k+1 (t) = 2tT k (t) − T k−1 (t) k = 1, 2, .…”

Section: Introductionmentioning

confidence: 99%

A new estimate for a quantity involving the Chebyshev polynomials of the first kind

Zhang

2019

Journal of Mathematical Analysis and Applications

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Section: Introductionmentioning

confidence: 99%

A new estimate for a quantity involving the Chebyshev polynomials of the first kind

Zhang

2019

Journal of Mathematical Analysis and Applications

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An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials

Altınkaya

2020

Mathematica Slovaca

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AbstractIn this present investigation, we will concern with the family of normalized analytic error function which is defined by$$\begin{array}{} \displaystyle E_{r}f(z)=\frac{\sqrt{\pi z}}{2}\text{er} f(\sqrt{z})=z+\overset{\infty }{\underset {n=2}{\sum }}\frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}. \end{array}$$By making the use of the trigonometric polynomials Un(p, q, eiθ) as well as the rule of subordination, we introduce several new classes that consist of 𝔮-starlike and 𝔮-convex error functions. Afterwards, we derive some coefficient inequalities for functions in these classes.

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Generation of New Operational Matrices for Derivative, Integration and Product by Using Shifted Chebyshev Polynomials of Type Four

Chishti¹

2021

JMCMS

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While solving the fractional order differential equation the requirement of the higher-order derivative is obvious therefore, this paper gives a definite expression for constructing the operational matrices of derivative which is the direct method to find the derivative of higher-order according to the requirement of the total differential equation. The proposed work expands the Chebyshev polynomial of type four up to six degrees that could help get the accuracy for the numerical solution of a given differential equation. Previously Chebyshev polynomial of the third type has been used by cutting the domain from [-1, 1] to [0, 1]. This study also generates the integrational operational matrix for solving the integral equation as well as an integrodifferential equation by using the Chebyshev polynomial of type four and expand it up to six order and generate the matrix by cutting the domain from [-1, 1] to [0, 1]. This is the first attempt to generate an integrational operational matrix that has never been highlight nor generate by any researcher. Another contribution of this paper is the generation of categorical expressions for the product of two Chebyshev vectors that will help in solving the differential equation of several kinds.

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An Extension of the Chebyshev Polynomials

Cited by 4 publications

References 22 publications

A new estimate for a quantity involving the Chebyshev polynomials of the first kind

A new estimate for a quantity involving the Chebyshev polynomials of the first kind

An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials

Generation of New Operational Matrices for Derivative, Integration and Product by Using Shifted Chebyshev Polynomials of Type Four

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