GENERALIZED EQUIDISTANT CHEBYSHEV POLYNOMIALS AND ALEXANDER KNOT INVARIANTS

We introduce the generalized equidistant Chebyshev polynomials T-(k,T-h) of kind of hyperkind h, where k, h are positive integers. They are obtained by a generalization of standard and monic Chebyshev polynomials of the first and second kinds. This generalization is fulfilled in two directions. The horizontal generalization is made by introducing hyperkind h and expanding it to infinity. The vertical generalization proposes expanding kind k to infinity with the help of the method of equidistant coefficients. Some connections of these polynomials with the Alexander knot and link polynomial invariants are investigated.