Resumo
We study the convergence of a group of solutions in series of confluent hypergeometric functions for theconfluent Heun equation. These solutions are expansions in two-sided infinite series (summation from minusto plus infinity) which are interpreted as a modified version of expansions proposed by Leaver [E. W. Leaver,J. Math. Phys. 27, 1238 (1986)]. We show that the two-sided solutions yield two nonequivalent groups ofone-sided series solutions (summation from zero to plus infinity). In the second place, we find that one-sidedsolutions of one of these groups can be used to solve an equation which describes a time-dependent two-levelsystem of Quantum Optics. For this problem, in addition to finite-series solutions, we obtain infinite-serieswavefunctions which are convergent and bounded for any value of the time t, and vanish when t goes to infinity.
