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The violation of a uniqueness theorem and an invariant in the application of Poincaré--Perron theorem to Heun's equation (1605.08960v4)
Published 29 May 2016 in math.CA, math-ph, and math.MP
Abstract: The domain of convergence of a Heun function obtained through the Poincar\'{e}--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.
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