We set (as usual) $\displaystyle{x \choose k} := \frac{x \cdot (x-1) \cdots (x-k+1)}{k!}$ for $x\in \mathbb{C}$.
Now we can define a function
$\displaystyle f(x) := \sum\limits_{k=0}^\infty {x \choose k}$.
Does anybody know how this function is called (I need its name, so that I can get more information about it)? I believe, it should be well-known, but I don't know its name.
Note that if we defined $\displaystyle{x \choose k} := \frac{x^k}{k!}$ instead, we would simply get the $\exp$ function - so my function is probably be related to it.