A generalization of Laguerre's theorems on zeros of entire functions
Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 855-863
Cet article a éte moissonné depuis la source Math-Net.Ru
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.
@article{MZM_1997_61_6_a5,
author = {S. G. Merzlyakov},
title = {A generalization of {Laguerre's} theorems on zeros of entire functions},
journal = {Matemati\v{c}eskie zametki},
pages = {855--863},
year = {1997},
volume = {61},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a5/}
}
S. G. Merzlyakov. A generalization of Laguerre's theorems on zeros of entire functions. Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 855-863. http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a5/
[1] Titchmarsh E., Teoriya funktsii, Nauka, M., 1980 | Zbl
[2] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956
[3] Kazmin Yu. A., “Ob odnoi zadache Gelfonda–Ibragimova, II”, Vestn. MGU. Ser. 1. Matem., mekh., 1965, no. 6, 37–44 | MR | Zbl
[4] Polia G., Sege G., Zadachi i teoremy iz analiza, Ch. 2, Nauka, M., 1978