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arXiv · 2201.03009

Harmonic Schwarzian derivative and methods of approximation of zeros

María J. Martín
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Abstract

We review the relation between the classical formulas of the pre-Schwarzian and Schwarzian derivatives of locally univalent analytic functions and the derivatives of the generating functions of the methods due to Newton and Halley, respectively, for approximating zeros. We extend these relations to the cases when the functions considered are harmonic.

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María J. Martín. 2022-01-09. Harmonic Schwarzian derivative and methods of approximation of zeros. https://arxiv.org/abs/2201.03009

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