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complex base tetration program
#5
Beautiful job, Sheldon!
If you put points uniformly at the circle around exp(1/e),
then with few points, you can get a good precision evaluating the derivatives of tet_b(z) with respect to b by the Cauchi contour integral. So. you can plot, for example,
d tet_b(z) / db,
d^2 tet_b(z) / db^2,
as functions of z, and make conclusion about the behavior in vicinity of b=exp(1/e).

I try to guess the result:
As b approaches exp(1/e), the quasiperiods become large; so, all the cut lines at the z plane are far away from zero (and out of the field of your pics). In this sense, in vicinity of b=exp(1/e), there should be no cutlines at all, so, b=exp(1/e) is regular point for the most of values of z. Do your evaluations allow to confirm or to refute such a guess?

Is your evaluation for fixed b and various z faster than evaluation for fixed z and varable b?
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Messages In This Thread
complex base tetration program - by sheldonison - 02/29/2012, 10:28 PM
RE: complex base tetration program - by Kouznetsov - 03/01/2012, 12:04 PM
RE: complex base tetration program - by mike3 - 03/10/2012, 06:59 AM
RE: complex base tetration program - by mike3 - 03/11/2012, 12:27 AM
RE: complex base tetration program - by Gottfried - 02/06/2016, 01:37 AM
RE: complex base tetration program - by Gottfried - 02/06/2016, 05:36 PM
RE: complex base tetration program - by Gottfried - 02/07/2016, 05:27 AM
RE: complex base tetration program - by Gottfried - 02/07/2016, 01:25 PM
RE: complex base tetration program - by Gottfried - 10/24/2016, 11:50 PM
RE: complex base tetration program - by Gottfried - 10/26/2016, 10:02 AM

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