Abstract
The partial expansions of the two-centre Coulomb Green's function in terms of Coulomb spheroidal functions are obtained. Two types of expansions are built for regular and irregular radial Coulomb spheroidal functions in terms of the usual radial Coulomb functions and in terms of the solutions of the confluent hypergeometric equation. For the coefficients in these expansions, relatively simple three-term recurrence relations have been obtained; these relations are finite difference analogues of second-order differential equations. The calculation of the acceptable values νmℓ that single out the minimal solutions of the mentioned finite-difference equations and ensure convergence of the constructed expansions has been implemented by using the continued fractions method.
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