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) ∫<sub>L</sub> (f(z)/(z-α)) dz.
Our approximations shall be of the form
Q(f) = Σ<sub>k=1</sub><sup>n</sup> A<sub>k</sub>f(τ<sub>k</sub>).
We characterize the nodes τ₁, τ₂, …, τ<sub>n</sub>, 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.