bo198214 Wrote:Thats interesting! Can you give a proof for n=0, i.e that
\( \lim_{n\to 0} \sqrt[n]{\frac{a_1^n+\dots+a_m^n}{m}} = \sqrt[m]{a_1 \dots a_m} \)?
Erm... no. Hasn't this already been proven somewhere?
bo198214 Wrote:So the formula \( \sqrt[c(2-x)]{x(2^{c(2-x)}-1)+1} \) is the generalized mean of what? *headscratch*
It should merely interpolate 2^^x between x=0 and x=1 - the graph seemed smooth enough (together with the other iterated values beyond) to assume it represented the actual values to at least four decimal digits, but in other tables I've seen, only three decimal digits match.
Perhaps it's just my light-hearted view on all these numbers...
By the way, I achieved slightly better results when I changed that n=0.345627(2-x) into n=0.691-0,3450832*x. Gosh, I think this is getting a bit out of hand here...