The infinitesimal behavior of the sum of Cauchy kernels and its derivative at infinity

Vladimir Shemyakov

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arXiv · 2403.04152

The infinitesimal behavior of the sum of Cauchy kernels and its derivative at infinity

Vladimir Shemyakov

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Abstract

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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Vladimir Shemyakov. 2024-03-07. The infinitesimal behavior of the sum of Cauchy kernels and its derivative at infinity. https://arxiv.org/abs/2403.04152

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