Optimal quadrature formulas in the space $\widetilde{W_2}^{(m,m-1)}$of periodic functions

This paper is devoted to the process of finding the upper bound for the absolute error of the optimal quadrature formula in the space $\widetilde{W_2}^{(m,m-1)}$of real-valued, periodic functions. For this the extremal function of the quadrature formula is used. In addition, it is shown that the norm of the error functional for the optimal quadrature formula constructed in the space $\widetilde{W_2}^{(m,m-1)}$ is less than the value of the norm of the error functional for the optimal quadrature formula in the Sobolev space $\widetilde{L_2}^{(m)}$.