On the construction of optimal quadrature formulas with equally spaced nodes

Abstract

In this paper in $S_2(P_2)$ Hilbert space the problem of construction of optimal quadrature formula in the sense of Sard is considered and using Sobolev's method a new optimal quadrature formula is obtained. For the optimal coefficients explicit formulas are given. Constructed optimal quadrature formula is exact for the functions $e^{-x}$ and $x e^{-x}$.