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

Rossi, John

doi:10.1090/S0002-9947-1982-0645337-X

The reciprocal of an entire function of infinite order and the distribution of the zeros of its second derivative
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Trans. Amer. Math. Soc. 270 (1982), 667-683 Request permission

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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Two problems in entire function theory

Reciprocals of entire functions of infinite order and functions extremal for the

theorem

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