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Transactions of the American Mathematical Society

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

 

 

Reality of the zeros of an entire function and its derivatives


Authors: Simon Hellerstein, Li Chien Shen and Jack Williamson
Journal: Trans. Amer. Math. Soc. 275 (1983), 319-331
MSC: Primary 30D20; Secondary 30D30, 30D35
DOI: https://doi.org/10.1090/S0002-9947-1983-0678353-3
MathSciNet review: 678353
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Abstract: In 1914 Pólya raised the problem of classifying the entire functions which together with all their derivatives have only real zeros. In earlier work Hellerstein and Williamson settled this problem for entire functions which are real on the real axis. We complete the classification in all cases and show that it is sufficient to consider the function and its first two derivatives.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0678353-3
Article copyright: © Copyright 1983 American Mathematical Society