New solutions of Heun general equation

Abstract

We show that in four particular cases the derivative of the solution of Heun general equation can be expressed in terms of a solution to another Heun equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behavior at only one of the singular points of the equation; the sum, however, has correct behavior.

Cited by in corpus (4)

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• Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
• A singular Lambert-W Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions
• Incomplete beta-function expansions of the solutions to the confluent Heun equation