论文标题
在收敛圆盘边界上的HEUN功能收敛的不可能。
Impossibility of convergence of a Heun function on the boundary of the disc of convergence
论文作者
论文摘要
Heun的方程式是二阶二阶方程，有四个常规的奇异性。 HEUN功能概括了众所周知的特殊功能，例如球形波，Lamé，Mathieu，超几何型函数等。系数的递归关系开始出现，通过将功率系列放入HEUN方程中。局部HEUN函数由其功率系列中的三个项复发关系组成，我们证明该函数不是在收敛光盘边界上收敛的。
The Heun's equation is the Fuchsian equation of second order with four regular singularities. Heun functions generalize well-known special functions such as Spheroidal Wave, Lamé, Mathieu, hypergeometric-type functions, etc. The recursive relation of coefficients starts to appear by putting a power series into the Heun equation. A local Heun function consists of the three term recurrence relation in its power series, and we prove that the function is not convergent on the boundary of the disc of convergence.
