Closed form analytical formulas for ground state energies in quantum Hall effect regime

Closed form analytical formulas are derived for both electron-electron and electron-background interaction energies at filling factors ν=1 and ν=1/(2s+1), integer s. Thus ground state energies are computed at ν=1 and ν=1/3 for systems with many electrons. The results agree well with those existing in the literature. Also, thermodynamic limit values for various energies are determined at unit filling factor as part of an analysis based on a large N expansion of various energies in powers of N, N being the number of electrons of the system.