Geodesic
The growth on a positive ray of entire functions with real Taylor coefficients
Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 577-588 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that if the Taylor coefficients of an entire transcendental function change sign sufficiently infrequently, then such a function increases on a positive ray in the same way as in the whole plane. 
@article{MZM_1973_14_4_a16,
     author = {A. I. Pavlov},
     title = {The growth on a~positive ray of entire functions with real {Taylor} coefficients},
     journal = {Matemati\v{c}eskie zametki},
     pages = {577--588},
     year = {1973},
     volume = {14},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a16/}
}
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A. I. Pavlov. The growth on a positive ray of entire functions with real Taylor coefficients. Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 577-588. http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a16/