(12/20/2009, 10:30 AM)Ansus Wrote: I do not understand what are you saying. Integral+cont. sum is not an inversion formula. Direct Taylor inversion, Lagrange inversion, polynomial inversion, rational inversion all diverge at those bases I suppose.
What I'm saying is this other formula doesn't seem to work where the integral/continuum-sum would, so I wasn't sure why you mentioned it.
And Andrew Robbins put together a wholly different approach, that converged to the inverse function (slog) for bases \( b > e^{1/e} \). The resulting powerseries did invert under the Lagrange theorem to yield the tetrational. So inversion does work, once you have a method that can yield the right powerseries to invert.
