Solving Second-Order Homogeneous Linear Differential Equations in Terms of the Tri-Confluent Heun's Function.

In this paper, we state an algorithm that checks whether a given second-order linear differential equation can be reduced to the tri-confluent Heun's equation. The algorithm provides a method for finding solutions of the form exp (∫ r (x) d x) · HeunT (q , α , γ , δ , ϵ , f (x)) , where the parameters α , β , λ ∈ C , the functions r , f ∈ C (x) , and f are not constant. [ABSTRACT FROM AUTHOR]