Combinatorial trigonometry with Chebyshev polynomials
نویسندگان
چکیده
منابع مشابه
Combinatorial Trigonometry with Chebyshev Polynomials
The Chebyshev polynomials have many beautiful properties and countless applications, arising in a variety of continuous settings. They are a sequence of orthogonal polynomials appearing in approximation theory, numerical integration, and differential equations. In this paper we approach them instead as discrete objects, counting the sum of weighted tilings. Using this combinatorial approach, on...
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The native mathematical language of trigonometry is combinatorial. Two interrelated combinatorial symmetric functions underlie trigonometry. We use their characteristics to derive identities for the trigonometric functions of multiple distinct angles. When applied to the sum of an infinite number of infinitesimal angles, these identities lead to the power series expansions of the trigonometric ...
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We study the asymptotic structure of polynomials with integer coef cients and smallest uniform norms on an interval of the real line Introducing methods of the weighted potential theory into this problem we improve the bounds for the multiplicities of some factors of the integer Chebyshev polynomials Introduction Let Pn C and Pn Z be the sets of algebraic polynomials of degree at most n respect...
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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...
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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.
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ژورنال
عنوان ژورنال: Journal of Statistical Planning and Inference
سال: 2010
ISSN: 0378-3758
DOI: 10.1016/j.jspi.2010.01.011