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Matematicheskie Zametki, 1997, Volume 61, Issue 6, Pages 855–863
DOI: https://doi.org/10.4213/mzm1569 (Mi mzm1569) 		 
A generalization of Laguerre's theorems on zeros of entire functions

S. G. Merzlyakov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
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DOI: https://doi.org/10.4213/mzm1569
Abstract: We prove some results generalizing the classical Laguerre theorems about the multiplicity and the number of zeros of the function
$$ \sum_{n=0}^\infty\varphi(n)\frac{f^{(n)}(0)}{n!}z^n, $$
Some specific applications are given.
Received: 10.02.1995
English version:
Mathematical Notes, 1997, Volume 61, Issue 6, Pages 717–723
DOI: https://doi.org/10.1007/BF02361213
Bibliographic databases:
UDC: 517.547.2
Language: Russian
Citation: S. G. Merzlyakov, “A generalization of Laguerre's theorems on zeros of entire functions”, Mat. Zametki, 61:6 (1997), 855–863; Math. Notes, 61:6 (1997), 717–723
Citation in format AMSBIB
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\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 6
\pages 717--723
\crossref{https://doi.org/10.1007/BF02361213}
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