A new asymptotic expansion is derived for the incomplete beta function I(a, b, x), which is suitable for large a, small b and $x > 0.5$. This expansion is of the form ...
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 ...
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