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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a property of rational functions. II


Author: Q. I. Rahman
Journal: Proc. Amer. Math. Soc. 40 (1973), 143-145
MSC: Primary 30A04
MathSciNet review: 0357746
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Abstract: It is shown that if $ {r_n}(z)$ is a rational function of degree $ n$ such that $ {r_n}(0) = 1,{\lim _{\vert z\vert \to \infty }}\vert{r_n}(z)\vert = 0$ and all its poles lie in $ \vert{\zeta _1}\vert \leqq \vert z\vert \leqq 1$ then $ {\max _{\vert z\vert = \rho < \vert{\zeta _1}\vert}}\vert{r_n}(z)\vert \geqq 1/(1 - {\rho ^n})$.


References [Enhancements On Off] (What's this?)

  • [1] Q. I. Rahman and Paul Turán, On a property of rational functions, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. (to appear).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0357746-7
PII: S 0002-9939(1973)0357746-7
Keywords: Rational functions, logarithmic derivative of a polynomial
Article copyright: © Copyright 1973 American Mathematical Society