Optimal Formulas for Calculating Linear Functionals

The main result of this work are the construction of composite optimal quadrature formulas in the Sobolev space of periodic functions. Here we find the optimal coefficients of the composite quadrature formulas at \(t=0,t=1,t=2\) for any \(m\geq 1\) . In addition, the norm of the error functionals of the constructed optimal quadrature formulas are calculated, i.e. the norms of optimal error functionals of composite quadrature formulas in the conjugate Sobolev space of periodic functions are obtained.