13 мая 2020 г. · Lower and upper bounds B_a(x) on the incomplete gamma function \Gamma(a,x) are given for all real a and all real x>0. These bounds B_a(x) are exact.

In this note, we prove upper and lower bounds for |Γ(a, z)| that are uniform in the region |z| > c|a − 1|, where c is a constant and both a and z are complex.

Similarly, the upper incomplete gamma function is defined as an integral from a variable lower limit to infinity. Definition · Properties · Continuation to complex values

7 апр. 2016 г. · 2 Answers. hence a simple upper bound is: Γ(x;a)≤axe−aa+1−x. That approximation can be refined, producing a continued fraction ... Are there well known lower bounds for the upper incomplete ... Upper bound for Gamma Function. - Math Stack Exchange Другие результаты с сайта math.stackexchange.com

16 июн. 2012 г. · Lower and upper bounds for the incomplete gamma function are also derived. Bounds for the error function erf are also established.

7 мая 2019 г. · I'm looking for some tight non asymptotic upper bound. The bound should be tight for both x→0 and x→∞. The tightness is not that stringent.

EXACT LOWER AND UPPER BOUNDS ON THE INCOMPLETE GAMMA FUNCTION. 1265 will transform a lower (respectively, upper) bound into an upper (respectively, lower).

Lower and upper bounds Ba(x) on the incomplete gamma function Γ(a,x) are given for all real a and all real x>0. These bounds Ba(x) are exact in the sense ...

Abstract. Lower and upper bounds $B_a(x)$ on the incomplete gamma function $\Gamma(a,x)$ are given for all real $a$ and all real $x>0$.

Iosif Pinelis, Exact lower and upper bounds on the incomplete gamma function, First abstract page, DOI, Find all available articles from these authors.