Geodesic
Some Properties of Entire Functions with Nonnegative Taylor Coefficients
Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 760-765.

Voir la notice de l'article provenant de la source Math-Net.Ru

If $f$ is an entire function of arbitrary finite order and with nonnegative Taylor coefficients, then we prove that its restriction to the positive part of the real axis belongs to de Haan's class $\Gamma$. We also show that $f/f'$ is a Beurling slowly varying function.
Keywords: entire function, regular variation, Beurling slow variation, de Haan's class $\Gamma$. 
@article{MZM_2007_81_5_a13,
     author = {S. Simich},
     title = {Some {Properties} of {Entire} {Functions} with {Nonnegative} {Taylor} {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {760--765},
     publisher = {mathdoc},
     volume = {81},
     number = {5},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a13/}
}
TY  - JOUR
AU  - S. Simich
TI  - Some Properties of Entire Functions with Nonnegative Taylor Coefficients
JO  - Matematičeskie zametki
PY  - 2007
SP  - 760
EP  - 765
VL  - 81
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a13/
LA  - ru
ID  - MZM_2007_81_5_a13
ER  - 
%0 Journal Article
%A S. Simich
%T Some Properties of Entire Functions with Nonnegative Taylor Coefficients
%J Matematičeskie zametki
%D 2007
%P 760-765
%V 81
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a13/
%G ru
%F MZM_2007_81_5_a13
S. Simich. Some Properties of Entire Functions with Nonnegative Taylor Coefficients. Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 760-765. http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a13/

[1] N. H. Bingham, C. M. Goldie, J. L. Teugels, Regular Variation, Encyclopedia of Mathematics and its Applications, 27, Cambridge Univ. Press, Cambridge, 1989 | MR | Zbl

[2] R. P. Boas, Entire Functions, Academic Press Inc. Publ., New York, 1954 | MR | Zbl

[3] S. Bloom, “A characterisation of $B$-slowly varying functions”, Proc. Amer. Math. Soc., 54 (1976), 243–250 | DOI | MR | Zbl

[4] S. I. Resnick, Extreme Values, Regular Variation and Point Processes, Applied Probability, 4, Springer-Verlag, New York–Berlin, 1987 | MR | Zbl

[5] M. R. Leadbetter, G. Lindgren, H. Rootzen, Extremes and Related Properties of Random Sequences and Processes, Springer Series in Statistics, Springer-Verlag, Berlin, 1983 | MR | Zbl

[6] G. H. Hardy, Orders of Infinity, Cambridge Univ. Press, Cambridge, 1924 | MR | Zbl

[7] G. Khardi, Dzh. Littlvud, G. Polia, Neravenstva, IL, M., 1948 | MR | Zbl