Geodesic
Regularly Varying Sequences and Entire Functions of Finite Order
Publications de l'Institut Mathématique, _N_S_67 (2000) no. 81, p. 31 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We present a method for estimating the asymptotic behavior of: $ f^\alpha(x):=\sum_{n=1}^\infty n^\alpha l_n a_n x^n, x\to \infty, \alpha \in R, $ related to a given entire function $f(x):=\sum_{n=1}^\infty a_n x^n$ of finite order $\rho$, $0\rho+\infty$, $a_n\ge 0$, $n\in N$; where $(l_n)$, $n\in N$, are slowly varying sequences in Karamata's sense.
Classification : 30D20 26A12 
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     author = {Slavko Simi\'c},
     title = {Regularly {Varying} {Sequences} and {Entire} {Functions} of {Finite} {Order}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {31 },
     publisher = {mathdoc},
     volume = {_N_S_67},
     number = {81},
     year = {2000},
     zbl = {1011.30025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2000_N_S_67_81_a3/}
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Slavko Simić. Regularly Varying Sequences and Entire Functions of Finite Order. Publications de l'Institut Mathématique, _N_S_67 (2000) no. 81, p. 31 . http://geodesic.mathdoc.fr/item/PIM_2000_N_S_67_81_a3/