Optimal quadrature formula with cosine weight function*

Аннотация

This paper studies the problem of construction of optimal quadrature formulas for approximate calculation of integrals with cosine weight in the Sobolev space. Here explicit formulas for the optimal coefficients are obtained. The obtained optimal quadrature formulas are exact for a polynomial of degree (𝑚−1). We study the order of convergence of the optimal formulas for the cases 𝑚 = 1,2.