Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 $f(z)$)?

share|cite|improve this question
Not 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 ... – Henning Makholm Oct 24 '11 at 16:08

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.