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 A system of functional equations for slog(x) ? tommy1729 Ultimate Fellow Posts: 1,625 Threads: 364 Joined: Feb 2009 07/18/2014, 12:23 PM Let x be a real number. Im looking for a real-analytic solution slog that satisfies : slog(1) = 0. slog(exp(x))= slog(x)+1. ??slog(??) = ??slog(??) And by those "??" I mean another functional equation on the real line such that slog is indeed real-analytic. I tried a few cases but it seems hard. A suggestion is limiting the range and domain by using slog(sin(x)^2) = ??? Actually I do not know any system of functional equations that gives a real-analytic nontrivial abel function. One easily gets contradictions with naive try-outs. It somewhat reminds of those attempts of making ackermann analogues analytic , and other similar hyperoperator ideas. slog(sin(x)^2) = slog(f(x)) - 1 however leads to f(x) = exp(sin(x)^2). Just to show how tricky it is. Nevertheless Im optimistic although that may be a bit crazy. regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread A system of functional equations for slog(x) ? - by tommy1729 - 07/18/2014, 12:23 PM RE: A system of functional equations for slog(x) ? - by tommy1729 - 07/18/2014, 09:58 PM RE: A system of functional equations for slog(x) ? - by jaydfox - 07/28/2014, 05:06 PM RE: A system of functional equations for slog(x) ? - by tommy1729 - 07/28/2014, 09:16 PM

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