Can you calculate Pi using a Solver?

[EdS2]

ah yes, like summation, integration certainly has ways to reach pi.

I'm still curious about the solver though. If any HP calculator's solver worked in the complex domain (and I imagine none do) then Euler's identity would give a route to pi.

(By the solver, I mean the facility which takes a function of one variable and finds a value of that variable which makes the function zero.)

As we know that pi isn't algebraic, it might be that we know there's no way to do this. But finding a fixed point of a recurrence feels a bit like finding a zero of a function, so I wonder if that could be a way.