(02/20/2013, 12:01 AM)bo198214 Wrote:(02/18/2013, 11:40 PM)mike3 Wrote: There is also the "continuum sum", the "matrix method" and the above mentioned Robbins' method (which you may be referring to). All five of these appear to yield the same result, but it is not proven, as far as I can tell. In theory, these should be able to define \( ^z a \) for any complex a and z. But the currently-available implementations only work for more limited ranges of bases a.
Ya, Andrew made a picture for the base ranges of the regular tetration (at the attracting fixpoint) and his tetration (which was called "natural tetration" at that time, we changed the nomenclature to "intuitive tetration") in this post. Unfortunately the server doesnt want to be crosslinked - and is down anyway - but I could download the picture and add it here in this post.
Yes, I forgot about that. Robbins' method does not in fact work for every base.
