Geodesic
Some Properties of Entire Functions with Nonnegative Taylor Coefficients
Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 760-765 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\Gamma$. 
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     author = {S. Simich},
     title = {Some {Properties} of {Entire} {Functions} with {Nonnegative} {Taylor} {Coefficients}},
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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