Generalized Equidistant Chebyshev Polynomials and Alexander Knot Invariants

  • A. M. Pavlyuk Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine

Abstract

We introduce the generalized equidistant Chebyshev polynomials T(k,h) of kind k 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.

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Published
2018-07-12
How to Cite
Pavlyuk, A. (2018). Generalized Equidistant Chebyshev Polynomials and Alexander Knot Invariants. Ukrainian Journal of Physics, 63(6), 488. https://doi.org/10.15407/ujpe63.6.488
Section
General physics