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The confluent Heun equation is one of 4 confluent forms of Heun'sdifferential equation in which is the Fuchsian equation of second order withfour regular singularities. A confluent Heun function is applicable to diverseareas such as theory of rotating/non-rotating black hole, the gauge theories onthick brane words, Schr$\ddot{\mbox{o}}$dinger equation for hydrogen moleculeion in Stark effect and etc. The confluent Heun function consists of the threeterm recurrence relation in its power series, and we show that the function isdivergent on the boundary of the disc of convergence.

Impossibility of convergence of a confluent Heun function on the boundary of the disc of convergence