Large order perturbation theory for the Coulomb angular spheroidal equation

The nature of perturbation theory for the Coulomb angular spheroidal equation (CASE) is considered. It has been shown that along with the power members of approximately (1/4p)sup(k), p → infinity, there could be present approximately esup(-2sp) members and the integer of s >=1 in asymptotic expansion of eigenvalues. Coefficients of eigenvalue expansion into a power series of 1/4p have been found to be asymptotic by number, that allows to analyse the obtained CASE solutions for all the possible real values of the σ parameter. The results obtained are used for studying electron terms of the Z1eZ2 ion. A comparison with some numerical results are presented