On Entire Functions of Fast Growth
On Entire Functions of Fast Growth
Let \[ (\ast )\quad f(z) = \sum \limits _{n = 0}^\infty {{a_n}{z^{{\lambda _n}}}} \] be a transcendental entire function. Set \[ M(r) = \max _{|z| = r} |f(z)|,\; m(r) = \max _{n \geq 0} \{ |{a_n}|{r^{{\lambda _n}}}\} \] and \[ N(r) = \max _{n \geq 0} \{ {\lambda _n}|m(r) = …