Continuously Tracing the HyperPower function x^^y

Discussion in 'Maple' started by Ioannis, Oct 1, 2003.

  1. Ioannis

    Ioannis Guest

    There was a nice bonus on my construction for a Continuous Extension for
    the HyperPower operator, which I discovered only two days ago.

    The definition that I use, seems to produce an infinity of new shapes if
    one traces the hyperexponent continuously.

    For example, although (-1)^^n = -1, for all n in N, (so that the
    function (-1)^^y returns infinately often to -1) the behavior of (-1)^^y
    for values in between natural numbers appears to be quite complex.

    A couple of .GIF trace samples, along with a short cross-referenced
    indirect proof that lim[n->+oo]i^^n exists (by considering the traces of
    i^^y, y>=0), can be found at:

    <http://users.forthnet.gr/ath/jgal/math/exponents4.html#trace>

    in my Math section:

    <http://users.forthnet.gr/ath/jgal/math/>

    Enjoy the read.
     
    Ioannis, Oct 1, 2003
    #1
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