Abstract
The analytic continued-fractional formula for energies of the bound states in the harmonium potential V(r)=ar-1+br+cr2, as suggested by Singh et al. (1978, 1979) and criticised by Flessas (1982), is correct if and only if b>0. This is the special case of the more general result. The author extends the analytic construction of the Green function and the rigorous specification of its validity to the whole class of potentials with r2V(r)=polynomial in ralpha , alpha =positive rational number.