closed form for regular superfunction expressed as a periodic function

[mike3]

I'm kind of intrigued at actually having a closed form for a real valued superfunction, like sqrt(2). I'm guessing that the number of terms required for convergence gets extremely large as z increases. From the terms I computed a couple of days ago, it looks like the terms are decreasing exponentially, which means the series acts like it has a singularity. However, since the regular superfunction is entire, we must have convergence to infinity, so the terms must eventually decrease faster than exponentially.
- Sheldon

Or it does already, but just a wee bit faster than exponential. This makes me wonder about an interesting place for mathematical exploration: the behavior of entire functions given by a Taylor series whose terms' coefficients decay just a "wee" bit faster than exponential. As this example shows, such functions can have extremely complicated behavior (note the complicated "fractal structure" of the graphs of these superfunctions.).