Expansions of the solutions to the confluent Heun equation in terms of the Kummer confluent hypergeometric functions

Abstract

We examine the series expansions of the solutions of the confluent Heun equation in terms of three different sets of the Kummer confluent hypergeometric functions. The coefficients of the expansions in general obey three-term recurrence relations defining double-sided infinite series; however, four-term and two-term relations are also possible in particular cases. The conditions for left- and/or right-side termination of the derived series are discussed.