Geodesic
A generalization of Laguerre's theorems on zeros of entire functions
Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 855-863 
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/
@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/}
}
TY  - JOUR
AU  - S. G. Merzlyakov
TI  - A generalization of Laguerre's theorems on zeros of entire functions
JO  - Matematičeskie zametki
PY  - 1997
SP  - 855
EP  - 863
VL  - 61
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a5/
LA  - ru
ID  - MZM_1997_61_6_a5
ER  - 
%0 Journal Article
%A S. G. Merzlyakov
%T A generalization of Laguerre's theorems on zeros of entire functions
%J Matematičeskie zametki
%D 1997
%P 855-863
%V 61
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a5/
%G ru
%F MZM_1997_61_6_a5

Voir la notice de l'article provenant de 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.

[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