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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The reciprocal of an entire function of infinite order and the distribution of the zeros of its second derivative


Author: John Rossi
Journal: Trans. Amer. Math. Soc. 270 (1982), 667-683
MSC: Primary 30D35
DOI: https://doi.org/10.1090/S0002-9947-1982-0645337-X
MathSciNet review: 645337
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Abstract: Let $ f$ be a real entire function of infinite order whose zeros together with those of $ f'$ are all real. It is proved that $ (1/f)''$ has an infinity of nonreal zeros. The location of the zeros of $ f''$ and $ (1/f)''$ is also investigated. The result complements a finite order result of Hellerstein and Williamson.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0645337-X
Keywords: Real entire function, real meromorphic function, infinite order
Article copyright: © Copyright 1982 American Mathematical Society