We say that a monic polynomial with integer coefficients is polygomial if its each zero obtained by squaring the edge or diagonal of regular n-gon unit circumradius. find connections certain polygomials Morgan-Voyce polynomials and further Chebyshev second kind.

We construct an Alexander-type invariant for oriented doodles from a deformation of the Tits representation twin group and Chebyshev polynomials second kind. Like Alexander polynomial, our vanishes on unlinked with more than one component. also include values several doodles.

Odd degree Chebyshev polynomials over a ring of modulo 2 have two kinds of period. One is an “orbital period”. Odd degree Chebyshev polynomials are bijection over the ring. Therefore, when an odd degree Chebyshev polynomial iterate affecting a factor of the ring, we can observe an orbit over the ring. The “ orbital period ” is a period of the orbit. The other is a “degree period”. It is observe...

In this paper, we will derive the explicit formulae for Chebyshev polynomials of third and fourth kind with odd even indices using combinatorial method. Similar results are also deduced their r-th derivatives. Finally, some identities involving Fibonacci negative obtained.

In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interval ofintegration. The suggested method is based on the use of Taylor series expansion to overcome the singularity which le...

We give two recursive expressions for both MacWilliams and Chebyshev matrices. The expressions give rise to simple recursive algorithms for constructing the matrices. In order to derive the second recursion for the Chebyshev matrices we find out the Krawtchouk coefficients of the Discrete Chebyshev polynomials, a task interesting on its own.

In this paper we construct two types of Hessenberg matrices with the property that every weighted isobaric polynomial (WIP) appears as a determinant of one of them, and as the permanent of the other. Every integer sequence which is linearly recurrent is representable by (an evaluation of) some linearly recurrent sequence of WIPs. WIPs are symmetric polynomials written in the elementary symmetri...

Let μ be a probability measure on the real line with finite moments of all orders. Suppose the linear span of polynomials is dense in L(μ). Then there exists a sequence {Pn}∞ n=0 of orthogonal polynomials with respect to μ such that Pn is a polynomial of degree n with leading coefficient 1 and the equality (x − αn)Pn(x) = Pn+1(x) + ωnPn−1(x) holds, where αn and ωn are SzegöJacobi parameters. In...

We discuss Lagrange interpolation on two sets of nodes in two dimensions where the coordinates of the nodes are Chebyshev points having either the same or opposite parity. We use a formula of Xu for Lagrange polynomials to obtain a general interpolation theorem for bivariate polynomials at either set of Chebyshev nodes. An extra term must be added to the interpolation formula to handle all poly...