"Roland Franzius" <email@example.com> wrote in message news:firstname.lastname@example.org... > 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. > > Try > > alpha.wolfram.com > > plot EllipticF[x,1-10^-14] for 0<x<7pi > > Dirct URL > > http://www.wolframalpha.com/input/?i=plot+EllipticF[x%2C1-10^-14]+for+0%3Cx%3C7pi
Thanks. It may well have been derived from that. I had to plot a function y=f(x) myself on graph paper. I think we were going over our answers to the homework. I remember another student commenting that it had points of infinite as well as zero gradient.