  The confluent Heun equation is one of 4 confluent forms of Heun's
differential equation in which is the Fuchsian equation of second order with
four regular singularities. A confluent Heun function is applicable to diverse
areas such as theory of rotating/non-rotating black hole, the gauge theories on
thick brane words, Schr$\ddot{\mbox{o}}$dinger equation for hydrogen molecule
ion in Stark effect and etc. The confluent Heun function consists of the three
term recurrence relation in its power series, and we show that the function is
divergent on the boundary of the disc of convergence.
