论文标题
关于Heun功能的正规化
On regularization of the Heun functions
论文作者
论文摘要
在本文中，我们考虑了HEUN函数，这是Karl Heun于1889年引入的方程式的解决方案。Heun功能概括了许多已知的特殊功能，并出现在许多现代物理学领域。 [1]中描述了功能的评估。它基于由Frobenius方法得出的原点附近的局部功率序列解决方案，并分析延续到整个复合平面，并切成分支切割。但是，当两个局部解决方案之一应包含对数项时，可以在方程式的指数相关参数$γ$的整数中发生特殊情况。这也意味着HEUN的奇异行为在$γ$接近整数值时起作用。在这里，我们建议一种正则化的方法，并重新定义HEUN功能在整数值的某些元素中，其中新功能平稳地取决于参数。
In the paper we consider the Heun functions, which are solutions of the equation introduced by Karl Heun in 1889. The Heun functions generalize many known special functions and appear in many fields of modern physics. Evaluation of the functions was described in [1]. It is based on local power series solutions near the origin, derived by the Frobenius method, and analytic continuation to the whole complex plane with branch cuts. However, exceptional cases can occur at integer values of an exponent-related parameter $γ$ of the equation, when one of the two local solutions should include a logarithmic term. This also means singular behavior of the Heun functions as $γ$ approaches the integer values. Here we suggest a method of regularization and redefine the Heun functions in some vicinities of the integer values of $γ$, where the new functions depend smoothly on the parameter.
