I spent about a minute thinking about why (1) was necessary. It's because S = S (3 - 4S^2) has more than one root. So that makes me wonder what happens when you substitute (1') s(0) = sqrt(3)/2. Also: even as stated I don't think this suffices, because, for example, the function f(x) = sin(|x|) would also satisfy the functional equation. (That is, (3) never samples the other side of the origin.) On Fri, Dec 13, 2019 at 9:06 AM Bill Gosper <billgosper@gmail.com> wrote:
1) sin(0) := 0 and
2) |sin(x) - sin(y)| ≤ |x - y| and
3) sin(x) = sin(x/3) (3 - 4 sin(x/3)^2).
Note that 2) isn't even true, e.g. x=0, y=i. If this means "No", then what about for real z? —rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun