Yoon Seok Choun
Published 2018-03-05Version 1
Heun functions generalize well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric-type functions. They 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 the radius of convergence of the Heun function by rearranging the order of the terms in its power series. And we show why the Poincare-Perron (P-P) theorem is only available for the conditional convergence since it is applied to the Heun's equation. Moreover, we construct the revised Cauchy ratio test in which is suitable for the three term recurrence relation in a power series.
Comments: 63 pages, 3 figures
Impossibility of convergence of a Heun function on the boundary of the disc of convergence
On convergence and growth of sums $\sum c_k f(kx)$
Impossibility of convergence of a confluent Heun function on the boundary of the disc of convergence
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