The function Fn,l (r) ;the radial part of of the pseudo-wave function k (r, , ) is expressed in terms of ion-core
electron density, n,l (r) and its relation with the radial part Pn,l (r ) of Hartree- Fock wave function. A new mathematical
function psl (x) called as pseudo-spherical function has been developed which is similar to other mathematical functions, and
helpful in determining many types of electron densities.