+- Tetration Forum (https://tetrationforum.org)
+-- Forum: Tetration and Related Topics (https://tetrationforum.org/forumdisplay.php?fid=1)
+--- Forum: Mathematical and General Discussion (https://tetrationforum.org/forumdisplay.php?fid=3)
+--- Thread: the fraction iteration approximation of tetration (/showthread.php?tid=1818)
the fraction iteration approximation of tetration - Alex Zuma 2025 - 04/14/2026
we approximate the arbitrary base logarithm with a rational function, namely (ax+b)/(cx+d).
we choose a to be 2, b to be -2, c to be ln(a1), d to also be ln(a1)
a1 is the arbitrary base of the logarithm.
when we're done, we use the iteration formula for (ax+b)/(cx+d).
and we get this graph: https://www.desmos.com/calculator/x6malmxjzt