Regular polygons, Morgan-Voyce polynomials, and Chebyshev polynomials
نویسندگان
چکیده
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.
منابع مشابه
Generalizations of Modified Morgan-voyce Polynomials
In two recent articles [2] and [3], Ferri et al. introduced and studied the properties of two numerical triangles, which they called DFF and DFZ triangles. However, in a subsequent article, Andre-Jeannin [1] showed that the polynomials generated by the rows of these triangles are indeed the Morgan-Voyce polynomials Bn{x) and bn(x), whose properties are well known [10] and [11]; in fact, the pol...
متن کاملSome relations between Kekule structure and Morgan-Voyce polynomials
In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) Morgan-Voyce polynomial equal to the number of k-matchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zig-zag nonbranched catacondensed benzenid chains and Morgan-Voyce polynomials and between regularly zig-zag ...
متن کاملPolynomials Related to Generalized Chebyshev Polynomials
We study several classes of polynomials, which are related to the Chebyshev, Morgan-Voyce, Horadam and Jacobsthal polynomials. Thus, we unify some of well-known results.
متن کاملSymmetrized Chebyshev Polynomials
We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves alternate) result that their coefficients are non-negative. As a corollary we find that Tn(c cos θ) and Un(c cos θ) are positive definite functions. We further s...
متن کاملChebyshev Polynomials and Primality Tests
Algebraic properties of Chebyshev polynomials are presented. The complete factorization of Chebyshev polynomials of the rst kind (Tn(x)) and second kind (Un(x)) over the integers are linked directly to divisors of n and n + 1 respectively. For any odd integer n, it is shown that the polynomial Tn(x)=x is irreducible over the integers i n is prime. The result leads to a generalization of Fermat'...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Notes on Number Theory and Discrete Mathematics
سال: 2021
ISSN: ['1310-5132', '2367-8275']
DOI: https://doi.org/10.7546/nntdm.2021.27.2.79-87