toying with (1+s/n)^n and t(s) tommy1729 Ultimate Fellow     Posts: 1,493 Threads: 356 Joined: Feb 2009 11/22/2021, 11:25 PM The idea is to go experimental. We approximate exp(s) by using (1+s/n)^n. And perhaps later take n to +oo in the limit. t(s) = (1 + erf(s))/2. R_n(s) = n*(s^(1/n) - 1) then  f_n(s) = (1 + (f_n(s-1) * t(s))/n )^n. F_n(s) = lim m to +oo of R_n^[m] ( f_n(s + m) ) And then build the superfunctions from those. And then ofcourse we can ask the analogue typical questions. We could also test to which fixpoints it agrees. (1 + z/n)^n = z has most of its zero's with negative real part and most on an almost circle for large n btw. For n odd we have a real fixpoint and there are always zero's close to the pair of ln(z) = z.  Another benefit is ( for finite m at least ) we ( probably ) do not have log singularities but only root singularities. I have many more ideas but to avoid making assumptions and speculations I will stop here. Also this idea is something we ( top forum posters ) reached together and is partially very intuitive so I gave no name.   regards tommy1729 « Next Oldest | Next Newest »