We study generating functions for the number of permutations in S n subject to two restrictions. One of the restrictions belongs to S 3 , while the other belongs to S k. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind.

We construct an orthogonal wavelet basis for the interval using a linear combination of Legendre polynomial functions. The coefficients are taken as appropriate roots of Chebyshev polynomials of the second kind, as has been proposed in reference [1]. A multi-resolution analysis is implemented and illustrated with analytical data and real-life signals from turbulent flow fields.

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 this paper, we are going to solve a class of ordinary differential equations that its source term are rational functions. We obtain the best approximation of source term by Chebyshev polynomials of the first kind, then we solve the ordinary differential equations by using the Adomian decomposition method

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...

Riordan matrix methods and properties of generating functions are used to prove that the entries of two Catalan-type Riordan arrays are linked to the Chebyshev polynomials of the first kind. The connections are that the rows of the arrays are used to expand the monomials (1/2) (2x) and (1/2) (4x) in terms of certain Chebyshev polynomials of degree n. In addition, we find new integral representa...