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Second Order Linear Differential Polynomials and Real Meromorphic Functions

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Abstract

The main result determines all real meromorphic functions f of finite lower order in the plane such that f has finitely many zeros and non-real poles, while f′′ + a 1 f′ + a 0 f has finitely many non-real zeros, where a 1 and a 0 are real rational functions which satisfy a 1(∞) = 0 and a 0(x) ≥ 0 for all real x with |x| sufficiently large. This is accomplished by refining some earlier results on the zeros in a neighbourhood of infinity of meromorphic functions and second order linear differential polynomials. Examples are provided illustrating the results.

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  1. School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK

    J. K. Langley

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Langley, J.K. Second Order Linear Differential Polynomials and Real Meromorphic Functions. Results. Math. 63, 151–169 (2013). https://doi.org/10.1007/s00025-011-0179-9

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