On Jan 27, 5:48 pm, David C. Ullrich <dullr...@sprynet.com> wrote: > On Tue, 27 Jan 2009 09:39:43 EST, amy666 <tommy1...@hotmail.com> > wrote: > > > > > > >here i introduce a brute force / greedy algoritm to compute f(f(x)) = exp(x). > > >its works best outside the unit radius. > > >it is based upon the approximation below , and is trivial considering the approximation. > > >since , once we have a sequence of ever better getting approximations , taking that limit gives the desired result. > > >the approximations are also usefull because of computational boundaries. > > >the algoritm is the limit n -> oo > > >note that f(f(x)) = g(x) can be computed if g(0) = 0 > > >f(f(x)) = exp(x) - exp( -1 * 25^n * x^2 ) > > >examples : > > >n = 1 : > > >f(f(x)) = exp(x) - exp( -25 * x^2 ) > > >n = 2 : > > >f(f(x)) = exp(x) - exp( - 625 * x^2 ) > > >n = 3 : > > >f(f(x)) = exp(x) - exp( - 15625 * x^2 ) > > >.. > > >i , tommy1729 , am the first to invent this. > > Invent _what_?