The violation of a uniqueness theorem and an invariant in the application of Poincaré--Perron theorem to Heun's equation

Abstract

The domain of convergence of a Heun function obtained through the Poincaré--Perron (P--P) theorem is not absolute convergence but conditional one [2]. We show that a uniqueness theorem is not available if we apply the P--P theorem into the Heun's equation. We verify that the uniqueness theorem is only applicable when a local Heun function is absolutely convergent.

merged with arXiv:1803.03115

References in corpus (4)

• Kerr-de Sitter Greybody Factors via Isomonodromy
• Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces
• The generalized Heun equation in QFT in curved space-times
• Probability distribution function for reorientations in Maier-Saupe potential