Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 76, No. 508 (May 24, 1905), pp. 127-144 (18 pages) ...
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 ...