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Extended Levett trigonometric series. [PDF]
PLoS ONEAn extension of two finite trigonometric series is studied to derive closed form formulae involving the Hurwitz-Lerch zeta function. The trigonometric series involves angles with a geometric series involving the powers of 3.
Robert Reynolds
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Approximation on the regular hexagon
Journal of Numerical Analysis and Approximation Theory, 2020 The degree of trigonometric approximation of continuous functions, which are periodic with respect to the hexagon lattice, is estimated in uniform and Hölder norms.
Ali Guven
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Best approximation by «angle» and the absolute Cesàro summability of double Fourier series
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 This article is devoted to the topic of absolute summation of series or Cesaro summation. The relevance of this article lies in the fact that a type of absolute summation with vector index which has not been previously studied is considered.
S. Bitimkhan, O. Mekesh
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Integrated Geometric Optimal Control of Spacecraft Attitude and Orbit Based on
IEEE Access, 2023 A model predictive convex programming (MPCP) on $SE(3)$ parametrized by trigonometric series control is proposed in this paper, to solve the optimal control problem of spacecraft attitude orbit integration.
Zhongzhong Zheng +4 more
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Partial best approximations and the absolute Cesaro summability of multiple Fourier series
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 The article is devoted to the problem of absolute Cesaro summability of multiple trigonometric Fourier series. Taking a central place in the theory of Fourier series this problem was developed quite widely in the one-dimensional case and the fundamental
S. Bitimkhan, D.T. Alibieva
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Journal of Inequalities and Applications, 2016 An interplay between the sum of certain series related to harmonic numbers and certain finite trigonometric sums is investigated. This allows us to express the sum of these series in terms of the considered trigonometric sums, and permits us to find ...
Omran Kouba
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Rearrangements of Trigonometric Series and Trigonometric Polynomials [PDF]
Real Analysis Exchange, 2004 The paper is related to the following question of P.~L.~Ul'yanov: is it true that for any $2π$-periodic continuous function $f$ there is a uniformly convergent rearrangement of its trigonometric Fourier series? In particular, we give an affirmative answer if the absolute values of Fourier coefficients of $f$ decrease.
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Hardy-Littlewood theorem for series with general monotone coefficients
Қарағанды университетінің хабаршысы. Математика сериясы, 2018 In this work we study trigonometric series with general monotone coefficients. Also, we consider Lqϕ ( Lq ) space. In particular, when ϕ ( t ) ≡ 1 the space Lqϕ ( Lq ) coincides with Lq .
S. Bitimkhan
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A new note on factored infinite series and trigonometric Fourier series
Comptes Rendus. Mathématique, 2021 In this paper, we have proved two main theorems under more weaker conditions dealing with absolute weighted arithmetic mean summability factors of infinite series and trigonometric Fourier series.
Bor, Hüseyin
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Dual Trigonometrical Series [PDF]
Proceedings of the Glasgow Mathematical Association, 1959 In a recent joint paper with J. C. Cooke [1], we have given a method of determining the coefficients an in the “dual” Fourier-Bessel serieswhere −1 ≤p≤, F(r) is specified and αn is a positive root of Jv(αnα) = 0. This method reduced the problem to the solution of an infinite set of algebraical equations and it was shown that, under certain ...
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