2016-08-09 4:05 GMT+02:00 James McCartney <asy...@gmail.com>: > > > On Tue, Jul 5, 2016 at 2:42 PM, James McCartney <asy...@gmail.com> wrote: > >> In the same vein: a family of smoothed sawtooth waves >> >> f(x) = x - x^a >> > > changing this to : > > f(x) = x - sgn(x)*abs(x)^a > > allows 'a' to be continuously variable, not just an odd integer. > sgn(x) is the signum function. >
Let x=-1 and a=2: f(x) = x - x^a --> f(-1) = -1 - (-1^2) = -2 f(x) = x - sgn(x)*abs(x)^a --> f(-1) = -1 - sgn(-1)*abs(-1)^2 = 0 The results are different. --- Uli
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