Kouznetsov Wrote:Gottfried, may I postulate that \( \exp^0(t)=t \) and \( \exp^{-1}(t)=0 \) ? In this case, will be any difference between definiitons (1) and (2)?
Hmm, the difference should only appear for the limit-discussion. I don't know, how I should do a limit->infinity discussion, if the first value to be computed is already dependent on the limit-case itself.
The difference for the finite case, however, is only one of the notation, I think.
In the view of implementation 1) needs a stack-construct, which stacks up to the top, computes this, and then returns with updated values (for the infinite case the stack needed to be infinite and would never give partial evaluations) ; 2) could be implemented as a loop, beginning at the top-exponent x, and "appending bases" at each step. Partial evaluations include then the different(?) effects by different starting-values/top-exponents (and for the limit-case one could check, whether the partial evaluations would converge or diverge)
Gottfried Helms, Kassel