The Zeros of the Second Derivative of the Reciprocal of an Entire Function

Content Provider	Scilit
Author	Hellerstein, Simon Williamson, Jack
Copyright Year	1981
Description	Let $f$ be a real entire function of finite order with only real zeros. Assuming that $f'$ has only real zeros, we show that the number of nonreal zeros of $f''$ equals the number of real zeros of $F''$, where $F = 1/f$. From this, we show that $F''$ has only real zeros if and only if $f(z) = \exp (a{z^2} + bz + c)$, $a \geqslant 0$, or $f(z) = {(Az + B)^n}$, $A \ne 0$, $n$ a positive integer.
Related Links	https://www.ams.org/tran/1981-263-02/S0002-9947-1981-0594422-9/S0002-9947-1981-0594422-9.pdf
Ending Page	513
Page Count	13
Starting Page	501
ISSN	00029947
e-ISSN	10886850
DOI	10.2307/1998364
Journal	Transactions of the American Mathematical Society
Issue Number	2
Volume Number	263
Language	English
Publisher	Duke University Press
Publisher Date	1981-02-01
Access Restriction	Open
Subject Keyword	Logic Function Zeros Reciprocal Second Derivative 1/f Exp Integer Geqslant Finite
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics