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Computational Methods and Function Theory 8 (2008), No. 1, 1--14
Copyright Heldermann Verlag 2008

Meromorphic Solutions of a Differential Equation with Polynomial Coefficients

Gary G. Gundersen
ggunders@uno.edu , University of New Orleans, Department of Mathematics, New Orleans, Louisiana 70148, U.S.A.

[Abstract-pdf] [Abstract-ps]

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'=P0+P1f+...+Pnfn,   n≥3,
where each Pk is a polynomial and Pn≠0. The estimate for M depends only on n and the number d of distinct zeros of Pn, while the estimate for L depends only on d.

Keywords: Meromorphic solutions, rational solutions, linearly independent solutions, differential equation, polynomial coefficients.

MSC 2000: 34M05.

[FullText-pdf (289 K)] [FullText-ps (483 K)]