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

Abstract

Starting from equations obeyed by functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions. The first series applies single Beta functions as expansion functions, 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 produce series solutions in terms of other special functions. Two examples of such expansions in terms of the incomplete Gamma functions are presented

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Cited by in corpus (5)

• Schrödinger potentials solvable in terms of the general Heun functions
• Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients
• A conditionally integrable Schrödinger potential of a bi-confluent Heun class
• Semi-commuting and commuting operators for the Heun family
• Series solutions of confluent Heun equations in terms of incomplete Gamma-functions