01/07/2021, 09:53 AM
It's been a very long time since I've posted on this forum. I hope everyone is doing well, and I hope the old groups amongst us have each found cool things of their own. I've diverged from this forum; mostly because my mathematical motivations have moved away from studies of tetration (or similar subjects). But recently, I've written a self contained solution to tetration. It's been maybe three years in the making. I keep shrinking the requirements and arguments and fiddling with it; but at this point, three years in, I guess it's done. I think the best place to announce this theorem is on this aprocryphal tetration site.
For those who'd appreciate a holomorphic tetration; taking \( (-2,\infty) \to \mathbb{R} \) bijectively, and strictly monotonely; holomorphic on \( \mathbb{C} \) upto a nowhere dense set; I have one.
The paper below is fairly involved, despite being only fifteen pages. It is self contained; but elements involve more general ideas formed in other work. Nonetheless, there forms a novel tetration. And everything you need to prove that is in this paper. I hope you all enjoy if you read it.
TETRATION COMPLETE ARXIV FINAL.pdf (Size: 313.56 KB / Downloads: 1,523)
For those who'd appreciate a holomorphic tetration; taking \( (-2,\infty) \to \mathbb{R} \) bijectively, and strictly monotonely; holomorphic on \( \mathbb{C} \) upto a nowhere dense set; I have one.
The paper below is fairly involved, despite being only fifteen pages. It is self contained; but elements involve more general ideas formed in other work. Nonetheless, there forms a novel tetration. And everything you need to prove that is in this paper. I hope you all enjoy if you read it.
TETRATION COMPLETE ARXIV FINAL.pdf (Size: 313.56 KB / Downloads: 1,523)