Let $f={\sum }_{n=0}^{\infty }{a}_n{z}^n$ be an entire function which is not a polynomial. Is it true that if$$\underset{r\to \infty }{\lim }\frac{{\max }_n|a_n{r}^n|}{{\max }_{|z|=r}|f(z)|}$$exists then it must be $0$?