Extreme values and entire functions of finite order

Abstract

For an arbitrary entire function g of finite order and with non-negative Taylor coefficients, we shall prove that its restriction to the positive part of real axis belongs to de Haan's class Γ. It follows that the laws F1(x) = 1 - 1/g(x) and F2(x) = ∫-∞xdt/g( t )/C are in the domain of attraction of the double exponential law with explicitly given norming constants.