(07/04/2011, 01:28 AM)JmsNxn Wrote: Yes, you did show that and I do not mean to ignore your proof, but it's just no explanation for why the series still converges to \( e^x \cdot \ln(x) \) over a temporary domain. If it shouldn't by all means converge, and yet it still does, doesn't that merit some sort of credit or observation?
I posted a new message in the original thread. The series does not converge to \( e^x \ln(x) \), but a function that is asymptotic to it for large \( x \). I.e. the resemblance between the two is only an approximation, not an equality.
http://math.eretrandre.org/tetrationforu...86#pid6086