@article{ajna2016411,
author={{Boltaev, Nurali D. and Hayotov, Abdullo R. and Shadimetov, Kholmat M.},
title={Construction of Optimal Quadrature Formula for Numerical Calculation of Fourier Coefficients in Sobolev Space L<SUB>2</SUB><SUP>(1)</SUP>},
journal={American Journal of Numerical Analysis},
volume={4},
number={1},
pages={1--7},
year={2016},
url={http://pubs.sciepub.com/ajna/4/1/1},
issn={2372-2126},
abstract={In the present paper the optimal quadrature formula for approximate evaluation of Fourier coefficients <img src=image/abs1.png></img> is constructed for functions of the space <img src=image/abs2.png></img>. At the same time the explicit formulas for optimal coefficients, which are very useful in applications, are obtained. The obtained formula is exact for constant. In particular, as consequences of the main result the new optimal quadrature formulas for approximate evaluation of integrals <img src=image/abs3.png></img> and <img src=image/abs4.png></img> are obtained. Furthermore, the order of convergence of the constructed optimal quadrature formula is studied.},
doi={10.12691/ajna-4-1-1}
publisher={Science and Education Publishing}
}