Timeline for Zeros of the lower incomplete gamma function
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 3, 2019 at 12:49 | comment | added | reuns | Did you see anything on the zeros of the entire function $f(x)=\int_0^1 e^{-xt}t^{s-1}dt=x^{-s}\gamma(s,x)$, its Mellin transform being $\frac{\Gamma(z)}{z-s}$ this function has known-asymptotic on every ray from the origin, on $\Re(x) > 0$ it looks like $x^{-s}$ on $\Re(x)<0$ it looks like $e^{-x}$, thus the zeros get close to the imaginary axis where it is the Fourier transform of $t^{s-1}1_{t\in [0,1]}$ | |
| Mar 15, 2019 at 17:00 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
http --> https
|
| May 1, 2017 at 21:45 | comment | added | Carlo Beenakker | A note on the real zeros of the incomplete gamma function, Ian Thompson | |
| May 1, 2017 at 20:30 | comment | added | Tom Copeland | @CarloBeenakker, could you please give the title and author of your 2012 ref? I can't access the link. (Many links to papers become broken soon, so I'd suggest always providing the title and the author.) | |
| Jun 29, 2016 at 21:45 | comment | added | Carlo Beenakker | the most recent paper I know of is from 2012 --- only asymptotics | |
| Jun 29, 2016 at 21:33 | comment | added | user40845 | Thank you for the swift and detailed response. I'd looked at this resource a bit, it's how I found Franklin, and it has a wonderful description of the dynamics of the zeros. I was wondering though if any exact results had been derived for the structure of these trajectories, especially in the case $x=1$? | |
| Jun 29, 2016 at 21:25 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
added 158 characters in body
|
| Jun 29, 2016 at 21:17 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
added 535 characters in body
|
| Jun 29, 2016 at 21:01 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |