[stuck] On the functional equation of the slog : slog(e^z) = slog(z)+1 tommy1729 Ultimate Fellow Posts: 1,906 Threads: 409 Joined: Feb 2009 04/28/2014, 09:21 PM On the functional equation of the slog : slog(e^z) = slog(z)+1. Related : http://math.eretrandre.org/tetrationforu...850&page=2 ( post 15 mainly ) The issue is here that the functional equation cannot hold everywhere , see also the secondary fixpoints for example ( the related link above ). Also we want to avoid singularities. SO ultimately (imho) 2 questions : 1) when is a region A analytic ? 2) when does the functional equation hold ? And the point of this thread is mainly that the 2 question are related ! The key is the n th derivative : slog(exp(z)) = slog(z) + 1 DERIVATE slog'(exp(z)) exp(z) = slog'(z) 2nd derivative slog''(exp(z)) exp(z) + slog'(exp(z)) = slog''(z) [stuck] Sorry but this idea is a bit stuck. Its complicated. I will update when possible. Feel free to comment. regards tommy1729 tommy1729 Ultimate Fellow Posts: 1,906 Threads: 409 Joined: Feb 2009 04/28/2014, 09:23 PM Big question : what functional equations for slog(z) do we have in the branches near to the fundamental ?? regards tommy1729 « Next Oldest | Next Newest »

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