What does $\exp(f)$ mean?

Question

In several posts around this site, I have encountered the expression $\exp(x)$ where $x$ is an arbitrary expression. What does this notation mean?

Googling tells you the answer. : http://goo.gl/eBchVh -1 for no effort. — evil999man, May 21 '14 at 15:37
Generally, it means the result of evaluating the function $\exp$ at the value $f$. — , May 21 '14 at 15:38
@user31782 Of course, it's hard to give exactly $\frac{2}{5}$ of an upvote. — Aidan F. Pierce, May 22 '14 at 12:07

score 10 · Accepted Answer · answered May 21 '14 at 15:34

10

$\exp(x) = e^x{}{}{}{}{}{}{}{}{}{}{}{}{}$

It's often used when we have $\exp(f(x)) = e^{f(x)}$ and $f(x)$ is complicated function. The focus, then, becomes the function in the exponent of $e$ (not to mention that it helps readers to not have to squint to read, say when $f$ is a rational function, $e^{f(x)}$).

answered May 21 '14 at 15:34

amWhy

209,954

1

Also when the author prefers to think of $e^x$ "as a function" rather than as the exponentiation of a particular constant $e$. – Jack M May 21 '14 at 15:52

Hakim · Answer 2 · 2014-05-21T15:46:00.323

7

It denotes the exponential function with base $e$ defined as:

$$\exp(z):=e^z.$$

edited May 21 '14 at 15:46

answered May 21 '14 at 15:34

Hakim

10,213

score 3 · Answer 3 · answered May 21 '14 at 15:36

3

This is the exponential function. In other words, $$\mathrm{exp}\,(x)$$ is another way of writing $$e^x,$$ where $$e=2.7182818284590452353...$$

answered May 21 '14 at 15:36

Ubiquitous

170

score 1 · Answer 4 · answered May 21 '14 at 15:37

Usually $1+x+\frac{x^2}{2!} + \frac{x^3}{3!} + \ldots$, if $x$ is something that can be multiplies by itself, divided by an integer, finite sums are defined, and there is some notion of the sums convergence. It makes sense for all finite-dimensional matrices, some operators in infinite dimensional spaces and also for other things.

What does $\exp(f)$ mean?

4 Answers4