Some Identities Involving the Reciprocal Sums of One-Kind Chebyshev Polynomials

Some More Identities Involving Rational Sums

The representation of sums in closed form can in some cases be achieved through a variety of different methods, including transform techniques, W–Z methods, Riordan arrays and integral representations. The interested reader is referred to the works of Egorychev [2], Gould [3], Merlini, Sprugnoli and Verri [4], Petkovšek, Wilf and Zeilberger [5] and Sofo [6], [7] and [8]. Recently Diaz-Barrero e...

Some identities involving generalized Gegenbauer polynomials

Generalized Chebyshev polynomials of the second kind

We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis. These polynomials can be used to describe the approximation of continuous functions by Chebyshev interpolation and Chebyshev series and how to efficiently compute such approximations. We conclude the pap...

Some Identities and a Matrix Inverse Related to the Chebyshev Polynomials of the Second Kind and the Catalan Numbers

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 ...

Some Symmetric Identities involving a Sequence of Polynomials

In this paper we establish some symmetric identities on a sequence of polynomials in an elementary way, and some known identities involving Bernoulli and Euler numbers and polynomials are obtained as particular cases.