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Asymptotic behavior of discrete holomorphic maps z^c, log(z) and discrete Painleve transcedents

S. I. Agafonov
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Abstract

It is shown that discrete analogs of z^c and log(z) have the same asymptotic behavior as their smooth counterparts. These discrete maps are described in terms of special solutions of discrete Painleve-II equations, asymptotics of these solutions providing the behaviour of discrete z^c and log(z) at infinity.

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BibTeXRIS

S. I. Agafonov. 2005-01-22. Asymptotic behavior of discrete holomorphic maps z^c, log(z) and discrete Painleve transcedents. https://arxiv.org/abs/math/0501381

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