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On the zeros of solutions of certain linear differential equations

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Abstract

Suppose that the linear differential equation

$$w^{(k)}(z)+{\mathop \sum^{k-2}\limits_{j=0}}A_{j}(z)w^{(j)}(z)=0$$

is such that the Aj are entire of finite order, and that A0 is the dominant coefficient in terms of growth. The existence of a fundamental set of solutions each having few zeros is shown to imply that the order of A0 is a positive integer.

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Authors and Affiliations

  1. Department of Mathematics, University of Nottingham, NG7 2RD

    J. K. Langley

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  1. J. K. Langley
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Langley, J.K. On the zeros of solutions of certain linear differential equations. Results. Math. 29, 276–279 (1996). https://doi.org/10.1007/BF03322224

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  • DOI: https://doi.org/10.1007/BF03322224

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