Chebyshev polynomials
A non-linear approach with long range dependence based on chebyshev polynomials
... (1997), can provide a very flexible approximation of deterministic trends. With respect to the long range dependence we use a very general framework that allows the incorporation of one or more integer or fractional ...
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Identities of the Chebyshev Polynomials, the Inverse of a Triangular Matrix, and Identities of the Catalan Numbers
... Bell polynomials of the second kind and for the Euler numbers and polynomials, ...the Chebyshev polynomials, the inverse of a triangular ma- trix, and identities of the Catalan numbers, ...
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An Iterative method for Solving the Container Crane Constrained Optimal Control Problem Using Chebyshev Polynomials
... In this paper we extend our work in [12, 13] to handle nonlinear optimal control problems subject to terminal state constraints, state variables and control variables saturation constraints. After applying the iterative ...
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Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds
... two polynomials in terms of any given sequence of ...of Chebyshev polynomials of the first, third, and fourth kinds, which are different from the ones previously ...
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Some new identities of Chebyshev polynomials and their applications
... of Chebyshev polynomials, elementary methods, and combinational techniques to study the computational problem of one kind of convolution sums involving second kind Chebyshev polynomials, and ...
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Representing by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials
... (2n + α + β + 1)Γ (n + α + β + 1)Γ (n + 1) δ m,n . (1.32) The sums of finite products of Chebyshev polynomials of the first kind in (1.33) and those of Lucas polynomials in (1.34) are the two main ...
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Fractional Calculus for Solving generalized Abel’s Integral Equations using Chebyshev Polynomials
... The paper it organized the following way: In section , we present the fractional integral and derivative operators and some their properties . In section , we combined f ractional technique, Chebyshev ...
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Second Kind Shifted Chebyshev Polynomials for Solving the Model Nonlinear ODEs
... In this paper, we build the integral collocation method by using the second shifted Chebyshev polynomials. The numerical method solving the model non-linear such as Riccati differential equation, Logistic ...
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The Approximate Solution for Solving Linear Volterra Weakly Singular Integro-Differential Equations by Using Chebyshev Polynomials of the First Kind
... using Chebyshev polynomials of the first kind of degree n as basis function for approximating the solution of one weakly singular integro-differential equation: which is the ...of Chebyshev ...
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CONNECTION PROBLEM FOR SUMS OF FINITE PRODUCTS OF CHEBYSHEV POLYNOMIALS OF THE THIRD AND FOURTH KINDS
... of Chebyshev polynomials of the third and fourth kinds in terms of five classical orthogonal ...Jacobi polynomials which involve some terminating hypergeometric functions 2 F 0 , 2 F 1 , and 3 F 2 ...
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EXPRESSING SUMS OF FINITE PRODUCTS OF CHEBYSHEV POLYNOMIALS OF THE SECOND KIND AND OF FIBONACCI POLYNOMIALS BY SEVERAL ORTHOGONAL POLYNOMIALS
... Abstract. This paper is concerned with representing sums of finite prod- ucts of Chebyshev polynomials of the second kind and of Fibonacci poly- nomials in terms of several classical orthogonal ...
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Solution of Fractional Differential Equations By Adomian Decomposition Method With Chebyshev Polynomials
... ABSTRACT : We study the nonlinear fractional differential equations using Adomian Decomposition with Chebyshev polynomials. The source terms are represented in terms of Taylor series and Chebyshev ...
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Solution of Fractional Differential Equations By Adomian Decomposition Method With Chebyshev Polynomials
... ABSTRACT : We study the nonlinear fractional differential equations using Adomian Decomposition with Chebyshev polynomials. The source terms are represented in terms of Taylor series and Chebyshev ...
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Chebyshev Polynomials for Solving a Class of Singular Integral Equations
... During the last three decades, the singular integral equation methods with applications to several basic fields of engineering mechanics, like elasticity, plasticity, aerodynamics and fracture mechanics have been studied ...
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On Chebyshev polynomials and their applications
... As far as we know, it seems that nobody has studied these problems yet. In this paper, we shall use the properties of the Chebyshev polynomials of the first kind to obtain some closed formulas for the above ...
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Some properties of Chebyshev polynomials
... Chebyshev polynomials are of great importance in many areas of mathematics, particu- larly approximation ...these polynomials. Chebyshev polynomials defined on [–, ] are well ...
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REPRESENTING SUMS OF FINITE PRODUCTS OF CHEBYSHEV POLYNOMIALS OF THE FIRST KIND AND LUCAS POLYNOMIALS BY CHEBYSHEV POLYNOMIALS
... of Chebyshev poly- nomials of the first kind and Lucas polynomials and represent each of them in terms of Chebyshev polynomials of all ...
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REPRESENTING SUMS OF FINITE PRODUCTS OF CHEBYSHEV POLYNOMIALS OF THIRD AND FOURTH KINDS BY CHEBYSHEV POLYNOMIALS
... Abstract. Here we consider sums of finite products of Chebyshev polyno- mials of the third and fourth kinds. Then we represent each of those sums of finite products as linear combinations of the four kinds of ...
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Total characters and Chebyshev polynomials
... The total character τ of a finite group G is defined as the sum of all the irreducible characters of G. K. W. Johnson asks when it is possible to express τ as a polyno- mial with integer coefficients in a single irreducible ...
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Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials
... of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions asso- ciated with ...Bernoulli polynomials and obtain some identities ...
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