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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Real zeros of derivatives of meromorphic functions and solutions of second order differential equations


Authors: Simon Hellerstein, Li-Chien Shen and Jack Williamson
Journal: Trans. Amer. Math. Soc. 285 (1984), 759-776
MSC: Primary 30D35; Secondary 34A20
MathSciNet review: 752502
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Abstract: We classify all functions $ F$ meromorphic in the plane with only real zeros and real poles which satisfy the additional conditions that $ F^{\prime}$ has no zeros and $ F''$ only real zeros. We apply this classification, in combination with some earlier results, to the study of the reality of zeros of solutions of the equation $ w'' + H(z)w = 0,H$ entire.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0752502-1
PII: S 0002-9947(1984)0752502-1
Article copyright: © Copyright 1984 American Mathematical Society