Timeline for Non-asymptotic upper bound of right tail of Gamma function

10 events

when toggle format	what		by	license	comment
May 23, 2019 at 15:26	vote	accept	neverevernever
May 8, 2019 at 8:53	comment	added	juan		@neverevernever Since $\lim_{x\to0} \Gamma(a,x)=\Gamma(a)$. A good bound for $x<a$ is $\Gamma(a,x)\le \Gamma(a)$. Perhaps this can be improved, but only slightly when $x$ is near $0$.
May 7, 2019 at 22:42	comment	added	neverevernever		So is there some similar bound for $x<a$?
May 7, 2019 at 22:08	comment	added	Mark Fischler		Yes, but the problem posed does not stipulate that $x > a$, it asks for an upper bound good for all $x,a>0$.
May 7, 2019 at 22:04	comment	added	juan		@Mark Fischler The hypothesis of the theorem says x > a. Your values do not satisfy this condition.
May 7, 2019 at 21:56	comment	added	Mark Fischler		There is a problem with this answer for smallish $x$. For instance, at $a = 3$ and $x = 1.5$, we have $$3 e^{-1.5} (1.5)^2 < 1.5062 < 1.6176 < \Gamma(3,1.5)$$ You wanted an upper bound that works everywhere; this one does not.
May 7, 2019 at 20:30	comment	added	juan		I think that Gabcke has translated his thesis to English. But I do not find now a link. I have also a translation to Spanish.
May 7, 2019 at 20:29	comment	added	neverevernever		Thank you! That's not in English, which I guess is the reason I cannot find the result.
May 7, 2019 at 20:28	vote	accept	neverevernever
May 8, 2019 at 0:04
May 7, 2019 at 20:26	history	answered	juan	CC BY-SA 4.0