Andrew Robbins' Tetration Extension

[bo198214]

I will do some testing, but my hunch is that the series will still converge on the "correct" solution, despite your attempt to break the solution. Because the modification you made is convergent, it has no radius of convergence, and hence it does not introduce a "false" singularity.

I am not sure what you mean by false singularity and false function, and how you would introduce a singularity somewhere. Despite I am very interested in the results you will come up with.

I also would suggest to stop calling one solution as being "correct" (as it doesnt fit the meaning of the word), I rather would suggest to call the solution gotten by Andrew's method as being "natural".