Some monotonicity and limit results for the regularised incomplete gamma function
Volume 94 / 2008
Annales Polonici Mathematici 94 (2008), 283-291
MSC: Primary 33B15; Secondary 62H12.
DOI: 10.4064/ap94-3-7
Abstract
Letting $P(u,x)$ denote the regularised incomplete gamma function, it is shown that for each $\alpha \geq 0$, $P(x,x+\alpha )$ decreases as $x$ increases on the positive real semi-axis, and $P(x,x+\alpha )$ converges to $1/2$ as $x$ tends to infinity. The statistical significance of these results is explored.
