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Starting from equations obeyed by functions involving the first or the secondderivatives of the biconfluent Heun function, we construct two expansions ofthe solutions of the biconfluent Heun equation in terms of incomplete Betafunctions. The first series applies single Beta functions as expansionfunctions, while the second one involves a combination of two Beta functions.The coefficients of expansions obey four- and five-term recurrence relations,respectively. It is shown that the proposed technique is potent to produceseries solutions in terms of other special functions. Two examples of suchexpansions in terms of the incomplete Gamma functions are presented

Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions