SIAM Journal on Applied Mathematics, Vol. 18, No. 4 (Jun., 1970), pp. 721-737 (17 pages) The probability density functions of products of independent beta, gamma and central Gaussian random variables ...

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 ...