We present a numerical approach to the central two-point connection problem for the confluent cases of the Heun class of differential equations. The crucial step is an ansatz for the solutions of the equations in terms of a generalized power series (called Jaffé expansions). It is shown that the resulting difference equations for the coefficients of these series are of Poincaré-Perron type. A (formal) asymptotic investigation of the solutions of these difference equations yields the exact eigenvalue condition.