Timeline for An explicit series representation for the analytic tetration with complex height
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
|
|
| Jan 25, 2017 at 1:06 | comment | added | user78249 | @Sheldon So I posted the question if $\lambda^{z}\phi(z)$ can be completely monotonic if $\phi$ isn't constant and I got an answer affirming that $\phi$ must be constant. | |
| Jan 23, 2017 at 4:24 | history | edited | user78249 | CC BY-SA 3.0 |
deleted 15 characters in body
|
| Jan 19, 2017 at 21:51 | history | bounty ended | Vladimir Reshetnikov | ||
| Jan 15, 2017 at 17:47 | comment | added | user78249 | Never mind, I had a flaw in my reasoning, I can't even show that :/ I over extended my reach a bit. Essentially I was switching to $\lambda^{-z}\phi(-z)$ and showing this can't have all positive Taylor coefficients. But I think now that this might be possible :S | |
| Jan 15, 2017 at 5:03 | comment | added | Sheldon | How do you prove the simplest case $\lambda^{z+\theta(z)}$ is only fully monotone if $\theta(z)$ is a constant? I know that the product of two monotone functions is monotone, but that doesn't tell you that the product of a monotone with a non-monotone is non-monotone. Do you have that as a known theorem? | |
| Jan 15, 2017 at 4:57 | comment | added | Sheldon | I like your usage of Ramanujan's master theorem, which provides a clear uniqueness condition. I'm not sure about your proof above. btw, I think I only proved that the inverse Schroder function is sort of monotonic at x=0, not necessarily at other values of x; with $a_n(-1)^n<0$. But the super-function is fully monotonic at the real axis. | |
| Jan 12, 2017 at 22:59 | comment | added | user78249 | Yeah, I wasn't certain, but I think this is at least a good layout on how to show it. I tried three different ways and they all seemed to break down, but this one seemed the most promising. | |
| Jan 12, 2017 at 22:51 | comment | added | Sheldon | I need sometime to think about it -- but I upvoted you. | |
| Jan 12, 2017 at 21:19 | history | answered | user78249 | CC BY-SA 3.0 |