Abstract
<jats:p>Fourier integrals of functions appear primarily in the theory of special functions and Fourier analysis, but also in other applied and computational sciences and engineering, such as theoretical physics, acoustic scattering, quantum chemistry, transport theory, electromagnetism, telecommunications, mechanics, and others. This paper considers the problem of finding the coefficients of weighted optimal quadrature formulas. First, we solve the boundary value problem for the extremal function of the quadrature formula. Using the extremal function, we find the norm of the error functional. The norm of the error functional depends on the coefficients and nodes. Using the Lagrange method, we obtain a system of linear algebraic equations for finding the coefficients of weighted optimal quadrature formulas.</jats:p>