The boundary-value problem for the spheroidal Coulomb equation for pure imaginary variable with homogeneous boundary conditions is considered. If the charge parameter is equal to zero the equation becomes spheroidal and then one can expand the eigenfunctions in power series. The series coefficients are bound by four member recurrence and Poincare-Perron - like relation. The series convergence is discussed. The elementary singular points case when the eigenfunction expansion in power series is possible is considered separately. The series coefficients are bound by three member recurrence relation. The numerically durable algorithm is based on these expansions by 1/N-method analogy.