Affiliation:
1. Mathematics Department, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Abstract
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)dx)·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.
Funder
King Saud University, Riyadh, Saudi Arabia
Reference23 articles.
1. Ronveaux, A. (1995). Heun’s Differential Equations, Oxford University Press.
2. Fiziev, P. (2015). The Heun functions as a modern powerful tool for research in different scientific domains. arXiv.
3. Heun functions and some of their applications in physics;Adv. High Energy Phys.,2018
4. Analytic solutions of the quantum two-state problem in terms of the double, bi-and triconfluent Heun functions;Shahverdyan;J. Contemp. Phys. Armen. Acad. Sci.,2015
5. Debeerst, R., van Hoeij, M., and Koepf, W. (2008, January 20–23). Solving differential equations in terms of Bessel functions. Proceedings of the Twenty-First International Symposium on Symbolic and Algebraic Computation, Linz/Hagenberg, Austria.