Abstract
This paper studies the problem of construction of optimal quadrature formulas for approximate calculation of integrals with trigonometric weight in the L(2m)(0, 1) space for any ω = 0, ω ∈ R. Here explicit formulas for the optimal coefficients are obtained. We study the order of convergence of the optimal formulas for the case m = 1, 2. The obtained optimal quadrature formulas are exact for Pm−1(x), where Pm−1(x) is a polynomial of degree (m − 1).
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