Exact Results in Quantum Theory & Gravity

We give a geometric interpretation about the method of resolving apparent singularities of Heun equations, a class of Fuchsian type linear differential equations. It turns out that the resolving singularity technique are used in various branches of applied mathematics and mathematical physics. We shall briefly introduce the use of Heun equations and its confluent counterparts in some of these applications. In particular, we apply the geometric interpretation in connecting the hypergeometric-type expansions solutions to Heun equations obtained by Erdelyi from the 1940s.
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