The radius of convergence of the Heun function

Abstract

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, and we show why the Poincare-Perron (P-P) theorem is not available for the absolute convergence since it is applied to the Heun's equation. Moreover, we construct the absolute convergence test in which is suitable for the three term recurrence relation in a power series.Comment: 14 pages. 3 figures. The number of pages has been reduced. Give the reader greater insight into what the key results are in the introduction. Correct some of the problems with Englis