If $f(z)$ is an entire function such that $$ \lim_{x \rightarrow -\infty}\frac{f(x)}{|f(x)|}=1$$ where $|f(x)|$ is the modulus of $f$, and $f(x)$ is just evaluating $f$ at real $x$. What can we say about $f(x)$ (or $f(z)$)?
Asked
Active
Viewed 719 times
4
-
9Not much. It could be the exponential function, or an even-degree polynomial with positive real leading coefficient, or $\cos z+2$, or $1/\Gamma(-z)$, or ... – hmakholm left over Monica Oct 24 '11 at 16:08