eng Science and Education Publishing American Journal of Numerical Analysis 2328-7292 2014-02-24 2 2 35 48 10.12691/ajna-2-2-2 AJNA2014222 article About Coefficients and Order of Convergence of the Optimal Quadrature Formula Aziz K. Boltaev 1 Abdullo R. Hayotov hayotov@mail.ru 1 Kholmat M. Shadimetov 1 Department of Computational Methods, Institute of Mathematics, National University of Uzbekistan, Do`rmon yo`li str. Tashkent, Uzbekistan In this paper we construct an optimal quadrature formula in the sense of Sard in the Hilbert space K2(P3). Using S.L. Sobolev's method we obtain new optimal quadrature formula and give explicit expressions for the corresponding optimal coefficients. Furthermore, we investigate order of convergence of the optimal formula. The obtained optimal quadrature formula is exact for the functions e-x, . http://pubs.sciepub.com/ajna/2/2/2/ajna-2-2-2.pdf optimal quadrature formulas error functional extremal function hilbert space optimal coefficients