I was wondering whether there exists a function that escapes to infinity with a finite input. For a specific example, how about $f(0)=0$ and as $x$ tends to $10$, $f(x)$ tends to infinity. The use of this would be to produce unimaginably large numbers with imaginable inputs.
If there are many such functions, I would prefer a formula which is short and snappy. If need be, magical operators such as an infinite sum or product would suffice. I understand that the tangent function has many poles (is that what you call an un-definition?), but they are sort of expensive to compute. I am not adept in calculus, but if you must... and at the very least I would like the function to be computable.
I am just a bit curious, is all. Can anyone help me? Perhaps the answer is obvious.