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An old new class of meromorphic functions

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Abstract

Based on the so-called rescaling method, we give a detailed description of the solutions of the Hamiltonian system (1) below, which was discovered only recently by Kecker and is strongly related to Painlevé’s fourth differential equation. In particular, the problem of determining those fourth Painlevé transcendents with positive Nevanlinna deficiency δ(0,w) is completely resolved.

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Authors and Affiliations

  1. Fakultät für Mathematik, Technische Universität Dortmund, D-44227, Dortmund, Germany

    Norbert Steinmetz

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  1. Norbert Steinmetz
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Correspondence to Norbert Steinmetz.

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Steinmetz, N. An old new class of meromorphic functions. JAMA 134, 615–641 (2018). https://doi.org/10.1007/s11854-018-0020-4

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  • DOI: https://doi.org/10.1007/s11854-018-0020-4

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