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Perspectives in Education, 2023 This article focuses on first-year university students’ understanding of concepts related to third-degree polynomial and trigonometric functions that they encountered during their study of Grade 12 mathematics.
Aneshkumar Maharaj
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Neighborliness of the symmetric moment curve [PDF]
, 2011 We consider the convex hull B_k of the symmetric moment curve U(t)=(cos t, sin t, cos 3t, sin 3t, ..., cos (2k-1)t, sin (2k-1)t) in R^{2k}, where t ranges over the unit circle S= R/2pi Z. The curve U(t) is locally neighborly: as long as t_1, ..., t_k lie
Alexander Barvinok +3 more
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Convergence of spectral decompositions of Hill operators with trigonometric polynomial potentials [PDF]
, 2009 We consider the Hill operator $$ Ly = - y^{\prime \prime} + v(x)y, \quad 0 \leq x \leq \pi, $$ subject to periodic or antiperiodic boundary conditions, with potentials $v$ which are trigonometric polynomials with nonzero coefficients, of the form (i ...
P. Djakov, B. Mityagin
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On generalized trigonometric functions and series of rational functions
, 2017 Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials, and the well known trigonometric functions can be seen to associate with polynomial $x^2-1$.
Yu, Han
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Integral method from even to odd order for trigonometric B-spline basis
AIMS MathematicsThe conventional trigonometric B-spline basis of odd order for piecewise trigonometric polynomial space possesses a lot of good modeling properties. However, its order cannot be increased by the integral method like B-spline because of the particularity ...
Mei Li, Wanqiang Shen
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A Levinson-Galerkin algorithm for regularized trigonometric approximation
, 1999 Trigonometric polynomials are widely used for the approximation of a smooth function $f$ from a set of nonuniformly spaced samples $\{f(x_j)\}_{j=0}^{N-1}$.
Strohmer, Thomas
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On a Fast Convergence of the Rational-Trigonometric-Polynomial Interpolation
Advances in Numerical Analysis, 2013 We consider the convergence acceleration of the Krylov-Lanczos interpolation by rational correction functions and investigate convergence of the resultant parametric rational-trigonometric-polynomial interpolation.
A. Poghosyan
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Covariance of the number of real zeros of a random trigonometric polynomial
International Journal of Mathematics and Mathematical Sciences, 2006 For random coefficients aj and bj we consider a random trigonometric polynomial defined as Tn(θ)=∑j=0n{ajcosjθ+bjsinjθ}. The expected number of real zeros of Tn(θ) in the interval (0,2π) can be easily obtained. In this note we show that this number is
K. Farahmand, M. Sambandham
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Bethe Equations "on the Wrong Side of Equator" [PDF]
, 1998 We analyse the famous Baxter's $T-Q$ equations for $XXX$ ($XXZ$) spin chain and show that apart from its usual polynomial (trigonometric) solution, which provides the solution of Bethe-Ansatz equations, there exists also the second solution which should ...
Baxter R J +10 more
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Approximation of classes B^ω_p,θ of periodic functions of several variables by polynomials with spectrum from cubic areas (in Ukrainian) [PDF]
Математичні Студії, 2011 We have obtained exact order estimates for error of approximation of classes B^ω_p,θ of periodic functions of several variables by trigonometric polynomials with spectrum from cubic areas.
S. A. Stasyuk
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