Узагальнені еквідистантні поліноми Чебишова і вузлові інваріанти Александера
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...
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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Publishing house "Academperiodika"
2018
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| Online Access: | https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2018043 |
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| Journal Title: | Ukrainian Journal of Physics |
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Ukrainian Journal of Physics| Summary: | 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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