We define the incomplete gamma function ratio for positive N by \begin{align*}\tag{1}P(N, b, X) &= \int^X_0 t^{N-1}e^{-bt} dt/ \int^\infty_0 t^{N-1}e^{-bt} dt ...

In the paper, the authors extend a function arising from the Bernoulli trials in probability and involving the gamma function to its largest ranges, nd logarithmically complete monotonicity of these ...