Heun functions generalize well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric-type functions. Heun functions are applicable to diverse areas such as theory of black holes, lattice systems in statistical mechanics, solutions of the Schrodinger equation of quantum mechanics, and addition of three quantum spins. We consider asymptotic behavior of Heun equation and the radius of convergence by rearranging the order of the terms in its power series. And we show why Poincare–Perron theorem is not always applicable to the Heun equation including linear homogeneous ODEs.
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