Geodesic
On power series whose tails have multiply positive coefficients
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 2, pp. 156-166 
Natalya Zheltukhina. On power series whose tails have multiply positive coefficients. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 2, pp. 156-166. http://geodesic.mathdoc.fr/item/JMAG_2003_10_2_a2/
@article{JMAG_2003_10_2_a2,
     author = {Natalya Zheltukhina},
     title = {On power series whose tails have multiply positive coefficients},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {156--166},
     year = {2003},
     volume = {10},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2003_10_2_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Entire functions whose tails have $4$-times positive coefficients are studied. The growth estimate for such functions is given. It is shown that the same growth estimate holds for entire functions of order $<1$ whose tails do not have zeros in the angle $\{z:|{\arg z}|\leq 4\pi /5\}$.