Taylor series of upx function

[bo198214]

I'm a hobby mathematician, taking fun on working on tetration. I would like to know if a Taylor series development exists for the ultra exponential function.
In my mind (correct me if I'm wrong), upx function as defined as the following:
- upx(1) = e
- upx(x+1) = exp ( upx(x) )

Hi Zagreus,

unfortunately there is no *the* tetration. There are several approaches how to define a Taylor-Series for tetration and it is not even clear whether some of them are equal as the coefficients are defined by limits and and even different solutions can come very close.
For the different approaches have a look into the FAQ and/or search the forum.