Approximating the function defined by discrete and integral conditions

The article deals with the problem of approximating the function in relation to which the values are known at some points (discrete conditions) and the values of integrals on certain intervals (integral conditions). The article states the task of finding a polynomial of a defined degree which brings nearer the defined conditions in the best way. The authors embed the dimensionless weight factor which allows to take into account the contribution of integral conditions into the total deficiency. The idea of this solution is based on the application of Gauss quadratures. The general formulas for finding the coefficients of approximating polynomials are obtained. The numerical examples illustrate the effect of weight factor on the result.