08/01/2009, 10:32 AM
(This post was last modified: 08/01/2009, 03:17 PM by sheldonison.)

I'm adding a graphs of sexp eta.upper, at the real axis and at imaginary=1. This is the same as Jay's cheta function. The function was shifted so that . I started with f(x) is approximately e*(1-(1/2x)), as x goes to -infinity, and optimized further by replacing x with a polynomial. I got this from the http://en.citizendium.org/wiki/Tetration web page. Anyway, taking the iterated of converges nicely at the real axis due to super exponential growth, but may not converge in the complex plane. At imaginary=1, the function gradually grows towards a real value of "e", as x goes to (imag=1, real=infinity).