Am 18.06.2014 19:39, schrieb John Smith: > A recent thread about points of inflection reminded me of a function I > encountered when I was a math student. > > The function had many points of inflection but it also had points, which I > presume are also called inflection points, where the gradient was infinite > (i.e tending to a vertical rather than horizontal line on an x,y graph). > > I remember the graph looking like a staircase with rounded edges but I have > completely forgotten what the function was. It's possible I have not > remembered it correctly due to it being so long ago. > > Can anyone tell me what this function was or give me a similar function?
A candidate is the elliptic integral of the first kind.
F(x,k) = int dphi 1/Sqrt(1-k sin^2 phi)
with k approaching 1 from below.
F represents the physical time as a function of the angle for a rotating mathematical pendulum nearly stopping indefinitely long times at the sequence of top dead centers phi= (2n+1) pi.