Abstract: Using the Hellman - Feynman （HF） and Hypervirial （HV） theorems, the perturbative coefficients of the eigenenergies are calculated in the case of Coulomb potential with a radial linear term and a constant term. The calculation method, excel to the usual Rayleigh- Schroedinger perturbation theory （RSPT）, does not require the calculation of eigenfunctions coefficients. This method is a fast and efficient tool for the calculation of large order eigenenergies coefficients.

Key words: perturbation theory, Coulomb potential, eigenenergies