Volodymyr Yu. LAZUR, Svitlana I. MYHALYNA  and  Mykhailo V. KHOMA
Uzhgorod National University,
Uzhgorod, UKRAINE
E-mail: lazur@univ.uzhgorod.ua, khoma@uzhgorod.ukrsat.com

The  Greenís  function for the two-center system with coulomb interaction

Semi-analytical representations (by the way of partial expansions) for a radial part of a Green's function for two identical Coulomb centers are obtained. Two types of expansions are built for regular and irregular radial Coulomb spheroidal functions: over the Coulomb radial functions and over the solutions of a confluent hypergeometric equation. The problem of convergence of these expansions is studied in detail and are explained formal fundamentalses of a computing procedure for solution to the related them infinite three-terms recurrent relations. The asymptotic formulas for permissible parameters n are obtained at R® 0 to within the O(R3) terms and at R® ¥ to within the O(1/R3) terms.