On power series whose tails have multiply positive coefficients - Zheltukhina, Natalya (Математическая физика, анализ, геометрия, 2003)
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:|z|4π/5}.