Optimal quadrature formula for approximate calculation of fourier coefficients in w2 (1,0) space

Аннотация

In the present paper the optimal quadrature formula for approximate evaluation of Fourier coefficients is constructed for functions of the space (1,0) 2 W [0,1] . At the same time the explicit formulas for optimal coefficients, which are very useful in applications, are obtained. The obtained formula is exact for the function exp(-x ) . Inparticular, as consequences of the main result the new optimal quadrature formulas for approximate evaluation of integrals are obtained