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Meromorphic Solutions of a Differential Equation with Polynomial Coefficients

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Abstract

We give new estimates for the maximum number M of distinct meromorphic solutions and also for the maximum number L of linearly independent meromorphic solutions of the first order differential equation

$$f^\prime = p_0+p_1f+...+p_nf^n,\ \ \ n\geq 3,$$

where each P k is a polynomial and P n ≢ 0. The estimate for M depends only on n and the number d of distinct zeros of P n, while the estimate for L depends only on d.

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Author notes

  1. Gary G. Gundersen

    Present address: , 2163 Idaho Falls Drive, Henderson, Nevada, 89044, USA

Authors and Affiliations

  1. Department of Mathematics, University of New Orleans, New Orleans, Louisiana, 70148, USA

    Gary G. Gundersen

Authors
  1. Gary G. Gundersen
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Correspondence to Gary G. Gundersen.

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Warmly dedicated to my friend, Walter Hayman

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Gundersen, G.G. Meromorphic Solutions of a Differential Equation with Polynomial Coefficients. Comput. Methods Funct. Theory 8, 1–14 (2008). https://doi.org/10.1007/BF03321665

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  • DOI: https://doi.org/10.1007/BF03321665

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