Abstract:
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 $\Gamma$.