Meromorphic Solutions of a Differential Equation with Polynomial Coefficients

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 where each P k is a polynomial and P n ≢ 0. The estimate for M depends only on n and the number d...

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Bibliographic Details
Published in:Computational methods and function theory 2008-05, Vol.8 (1), p.1-14
Main Author: Gundersen, Gary G.
Format: Article
Language:English
Subjects:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
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Summary: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 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 .
ISSN:1617-9447
2195-3724
DOI:10.1007/BF03321665