Removing the branch points in the base: a uniqueness condition? - Printable Version +- Tetration Forum ( https://math.eretrandre.org/tetrationforum)+-- Forum: Tetration and Related Topics ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)+--- Forum: Mathematical and General Discussion ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)+--- Thread: Removing the branch points in the base: a uniqueness condition? ( /showthread.php?tid=1075) |

Removing the branch points in the base: a uniqueness condition? - fivexthethird - 03/19/2016
In many cases, when dealing with the math behind tetration, a recurring feature is the logarithm of the fixed point multiplier , which I will call from here on Since the fixed point multiplier is determined by the base, is really just the base in disguise: But all three functions have branch points that correspond to the ones in tetration's base: the inner log to 0, the productlog to , the outer log to 1. Thus, I think that it's reasonable to desire the following to be the case for any reasonable tetration: Let x > 0 and tet(x,b) be our tetration solution. Then analytically continues to a function without branch points in So in other words, the branch we're on should entirely depend on what branches of those three functions we pick. |