柯西核之和及其导数在无穷远处的无穷小行为
The infinitesimal behavior of the sum of Cauchy kernels and its derivative at infinity
AI总结：
本研究针对函数在无穷远处极限不存在时的取值问题，基于Nevanlinna理论的平均研究思路，探讨收敛到极限概念的积分解释，并将其应用于柯西核之和及其导数的研究。
摘要：
在分析学中，了解函数在无穷远处的值通常十分有用，该运算具有良好的性质。然而，即便极限不存在，一些直观的考量也表明，函数在某种意义上仍在无穷远处取特定值。在Nevanlinna理论中，所有对象都是从平均意义上（即通过其积分）被研究的，因此收敛到极限这一概念的积分诠释对亚纯函数理论是有益的。这正是本工作的核心聚焦点，并将其应用于柯西核之和及其导数的研究。
英文摘要：
In analysis, it's often useful to know the value of a function at infinity, this operation possesses pleasant properties. However, even when the limit does not exist, some intuitive considerations may suggest that the function still assumes a specific value at infinity in a certain sense. In Nevanlinna theory, all objects are studied on average, i.e., their integrals, hence the integral interpretation of the concept of convergence to a limit is beneficial for the theory of meromorphic functions. This is precisely the focus of this work, applied to sums of Cauchy kernels and their derivatives.
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