10/01/2007, 12:57 PM

For the ongoing discussion about the best way to define a continuous version for the tetration it might be useful to have a look at the following article, which deals with the equivalent problem concerning the gamma-function. See Luschny's Factorial

Although the gamma-function is now well established, its definition as a continuous version of the factorial function has a history of controversity about what might be the most useful and most natural property to obtain by a certain type of interpolation. I'm unable to comment on this properly, but possibly the more experienced participiants of this forum can take some thing inspiring from this. Anyway - the glance, which I get from this text, makes me cautions with assumtions, that "my" preferred interpolation of tetration is the "most natural" or "only useful" one... ;-)

Gottfried

Although the gamma-function is now well established, its definition as a continuous version of the factorial function has a history of controversity about what might be the most useful and most natural property to obtain by a certain type of interpolation. I'm unable to comment on this properly, but possibly the more experienced participiants of this forum can take some thing inspiring from this. Anyway - the glance, which I get from this text, makes me cautions with assumtions, that "my" preferred interpolation of tetration is the "most natural" or "only useful" one... ;-)

Gottfried

Gottfried Helms, Kassel