Estimation of the error for the optimal quadrature formula in the Sobolev space W(2) 2 (0; 1)

In this paper, we consider the construction of an optimal lattice quadrature formula in the space W(m) 2 (0; 1). We derive an analytical expression for an error functional norm and obtain a system of linear equations of Wiener-Hopf type by the coefficients using the method of Lagrange multipliers. Further, we apply the Sobolev method to get the analytical representation of the optimal coefficients. Using these coefficients, we calculate the norm of the error functional of the optimal quadrature formula for m = 2 in W(m) 2 (0; 1) space.