The zeros of the second derivative of the reciprocal of an entire function
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- by Simon Hellerstein and Jack Williamson PDF
- Trans. Amer. Math. Soc. 263 (1981), 501-513 Request permission
Abstract:
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.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 263 (1981), 501-513
- MSC: Primary 30D30
- DOI: https://doi.org/10.1090/S0002-9947-1981-0594422-9
- MathSciNet review: 594422