My favourite is:

Does the exponential function have a square root?

I will give a comprehensive answer as soon as I got the time.

edit: Oh I see its similar to:

What’s a natural candidate for an analytic function that interpolates the tower function?

Where some people from our forum gave some hints already.

Does the exponential function have a square root?

I will give a comprehensive answer as soon as I got the time.

edit: Oh I see its similar to:

What’s a natural candidate for an analytic function that interpolates the tower function?

Where some people from our forum gave some hints already.