We give a method, by solving a nonlinear system of equations, for Gauss harmonic interpolation formulas which are useful for approximating, the solution of the Dirichlet problem. We also discuss approximations for integrals of the form I(f) = (1/2πi) ∫_L (f(z)/(z-α)) dz. Our approximations shall be of the form Q(f) = Σ_k=1ⁿ A_kf(τ_k). We characterize the nodes τ₁, τ₂, …, τ_n, to get the maximum precision for our formulas. Finally, we propose a general problem of approximating for linear functionals; our results need further development. / Ph. D.