Geodesic
A generalization of Laguerre's theorems on zeros of entire functions
Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 855-863

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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},
     publisher = {mathdoc},
     volume = {61},
     number = {6},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a5/}
}
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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/