The Relation Between Chebyshev Polynomials and Jacobsthal and Jacobsthal Lucas Sequences

Year 2020, , 1162 - 1170, 01.12.2020

Şükran Uygun

https://doi.org/10.16984/saufenbilder.687708

Abstract

In this paper Jacobsthal, Jacobsthal Lucas and generalized Jacobsthal sequences are denoted by aid of first or second type of Chebyshev polynomials by different equalities. Then using these equalities a relation is obtained between Jacobsthal and generalized Jacobsthal numbers. Moreever, the nth powers of some special matrices are found by using Jacobsthal numbers or Chebyshev polynomials. Some connections among Jacobsthal, Jacobsthal Lucas are revealed by using the determinant of the power of some special matrices. Then, the properties of Jacobsthal, Jacobsthal Lucas numbers are obtained by using the identities of Chebyshev polynomials.

Keywords

Chebhshev polynomials, Jacobsthal Sequence, Jacobsthal Lucas Sequence

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