jaydfox Wrote:Note that if we flip this graph about the line y=x, we'll see the pentalog. There will be a logarithmic singularity at about x=1.850354529. We can calculate the base of the logarithm by dividing the differences of two consecutive pairs of integer pentates. Going out to -100 iterations, This yields a value of about 6.460671295681839390208370083.

Just numerology: Can it be :

pi*(e^(1/e))^2 = 6,55670879

and inverse 0,152516........?

I have plotted all 8 "spirals " of the form 4 : ( +-t^+-1/t), 4: (+- 1/t)^+-(t) in polar coordinates and there are certainly interesting forms , crossing points, and regions.

I do not know how to get image in here, but it is in the atachment.