Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University473210.18287/2541-7525-2012-18-3.1-5-13ABOUT ONE PROBLEM OF THE APPROXIMATION THEORYAbakumovYu.G.morenov.sv@ssau.ruVerhoturovaM.A.morenov.sv@ssau.ruKoganE.S.morenov.sv@ssau.ruChita State University01092012183.15130606201706062017Copyright © 2012, Abakumov Y., Verhoturova M., Kogan E.2012In the given article the solution of the problem of finding of accurate constants by methods of summation of Fourier series is considered. The number of results belonging to the constants , the existence of parameters are also set forth.methods of summation of Fourier series, trigonometric Bas cakov operators, accurate constants.