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

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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 $\Gamma$. 
@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/}
}
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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/