Construction of Optimal Quadrature Formulas Exact for Exponentional-trigonometric Functions by Sobolev’s Method

The paper studies Sard’s problem on construction of optimal quadrature formulas in the space W 2 (,0) by Sobolev’s method. This consists two parts: first calculating norm error functional and then finding minimum this coefficients formulas. Here is calculated with help extremal function. Then using method Lagrange multipliers system linear equations for obtained, moreover existence uniqueness solution are discussed. Next, discrete analogue Dm(hβ) differential operator $${{{d^{2m}}} \over {d{x^{2m}}}} - 1$$ constructed. Further, , which based Dm(hβ), described. m = 1 3 exact to exponential-trigonometric functions obtained. Finally, at end rate convergence (3,0) cases presented.