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Transactions of the American Mathematical Society

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

 

 

Inequalities satisfied by entire functions and their derivatives


Authors: Boo-sang Lee and S. M. Shah
Journal: Trans. Amer. Math. Soc. 149 (1970), 109-117
MSC: Primary 30.55
DOI: https://doi.org/10.1090/S0002-9947-1970-0257355-6
MathSciNet review: 0257355
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Abstract: For a class of entire functions with simple and positive zeros, it is shown that the maximum of the moduli of the first two Taylor coefficients at any point z, dominate all the remaining Taylor coefficients, provided $ \vert z\vert$ is sufficiently large. Further, there is a subclass for which this result holds at every point z.


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DOI: https://doi.org/10.1090/S0002-9947-1970-0257355-6
Keywords: Entire functions, canonical products, functions of bounded index
Article copyright: © Copyright 1970 American Mathematical Society