Numerical values of waw functions. calculated from Hartree-fock method. are nowadaysrnavailable for many atoms and ions. Analytical forms of these functions arernimportant in some cases. By studying Pron~"s method of representing numericalrnresults analytically into sums of exponentials. it is shown that it is possible to applyrnthe technique for approximating the numerically given radial part of atomic va'ernfunctions into sums of exponentials analytically. for each important step in Prony'srnmethod computer program is developed. The integrated program of the Prony'srnmethod is applied to the numerical radial self consistent field (SCf) wave functionsrnof a closed-shell Cd++ ion and the exponents and coefficients for the exponentialsrnof the approximated analytical functions are determined, Comparison between thernanalytical functions and the numerical functions show good agreement for 'a'ernfunctions with smaller principal quantum number value, , new algorithm for approximatingrntabulated numerical radial SCf atomic waw functions analytically intornsums of exponentials is introduced, , computer program is developed for the proposedrnnew algorithm and the technique is applied to ,Id function of cadmium ion.rnCd++. and to 2s and 2p functions of floride ion .f-. Exponents and coefficients ofrnthe exponentials of the approximating functions are determined. The approximatedrnanalytical forms of the numerical radial wave functions are used to reproduce numericalrnvalues of the function. The analytical and numerical functions are found to be inrngood agreement. These techniques can also be applied to analytically approximaternnllll1erical SCF functions of other ions