1. R. L. Adler & T. J. Rivlin. "Ergodic and Mixing Properties of Chebyshev Polynomials." Proa. Amer. Math. Soc. 15 (1964) :79'4-7'96. 2. P. Johnson & A. Sklar. "Recurrence and Dispersion under Iteration of Cebysev Polynomials." To appear. 3. C.H. Kimberling. "Four Composition Identities for Chebyshev Polynomials." This issue, pp. 353-369. 4. T. J. Rivlin. The Chebyshev Polynomials. New York: Wi...

Tthis paper, is concerned with obtaining numerical solutions for a class of convection-diffusion equations (CDEs) with variable coefficients. Our approaches are based on collocation methods. These approaches implementing all four kinds of shifted Chebyshev polynomials in combination with Sinc functions to introduce an approximate solution for CDEs . This approximate solution can be expressed as...

We analyze the asymptotic rates of convergence of Chebyshev, Legendre and Jacobi polynomials. One complication is that there are many reasonable measures of optimality as enumerated here. Another is that there are at least three exceptions to the general principle that Chebyshev polynomials give the fastest rate of convergence from the larger family of Jacobi polynomials. When f (x) is singular...

this paper presents an efficient modification of the variational iteration method for solvingboundary value problems using the chebyshev polynomials. the proposed method can be applied to linearand nonlinear models. the scheme is tested for some examples and the obtained results demonstrate thereliability and efficiency of the proposed method.

The Chebyshev-Boubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary Riordan arrays. Examples include the Chebyshev polynomials of the second kind and the Boubaker polynomials. We study the connection coefficients of this class of orthogonal polynomials, indicating how Riordan array techniques can lead to closed-form expressions for these connection...

The Chebyshev polynomials have many beautiful properties and countless applications, arising in a variety of continuous settings. They are a sequence of orthogonal polynomials appearing in approximation theory, numerical integration, and differential equations. In this paper we approach them instead as discrete objects, counting the sum of weighted tilings. Using this combinatorial approach, on...

Formulae expressing explicitly the coefficients of an expansion of double Jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. Extension to expansion of triple Jacobi polynomials is given. The results for the special cases of double and triple ultraspher...

In the paper, the authors establish two identities to express higher order derivatives and integer powers of the generating function of the Chebyshev polynomials of the second kind in terms of integer powers and higher order derivatives of the generating function of the Chebyshev polynomials of the second kind respectively, find an explicit formula and an identity for the Chebyshev polynomials ...

1. P. Bateman, J. Kalb, and A. Stenger, A limit involving least common multiples, this MONTHLY 109 (2002) 393–394. doi:10.2307/2695513 2. L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, D. Reidel, DordrechtHolland, 1974. 3. B. Farhi, Nontrivial lower bounds for the least common multiple of some finite sequences of integers, J. Number Theory 125 (2007) 393–411. doi:...