Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Successive derivatives of entire functions
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by Simon Hellerstein and Jack Williamson
Proc. Amer. Math. Soc. 66 (1977), 105-108
DOI: https://doi.org/10.1090/S0002-9939-1977-0460637-8

Abstract:

We show that if f is a real entire function which has, along with each of its derivatives, only real nonpositive zeros, then either $f(z) = c{e^{\sigma z}},c$ and $\sigma$ real constants, or \[ f(z) = c{z^m}{e^{\sigma z}}\prod \limits _n {\left ( {1 + \frac {z}{{|{z_n}|}}} \right )} \] where $\sigma \geqslant 0$ and $\sum \nolimits _n {|{z_n}{|^{ - 1}} < \infty }$.
References
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Bibliographic Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 66 (1977), 105-108
  • MSC: Primary 30A66
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0460637-8
  • MathSciNet review: 0460637