Formulas for approximate calculation of the Chebyshev coefficients

The approximate calculation of integrals is a common part of research in various fields of mathematics, primarily in the theory of approximations and computational mathematics. In turn, within the theory of numerical integration, distinctions take place depending on the features of the integrand, the scale of which is "Quadrature (cubature) formulas" and "Theory of oscillations". This article belongs to the second type of problems and consists in the approximate calculation of the Chebyshev coefficients.