# Meromorphic Solutions of a Differential Equation with Polynomial Coefficients

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 $$f^\prime = p_0+p_1f+...+p_nf^n,\ \ \ n\geq 3,$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

# Meromorphic Solutions of a Differential Equation with Polynomial Coefficients

, Volume 8 (1) – Mar 27, 2007
14 pages

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Publisher
Springer Journals
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321665
Publisher site
See Article on Publisher Site

### 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.

### Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 27, 2007

### References

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