This is a preview. Log in through your library . Abstract Mill's ratio can be expressed, for positive values of the argument x, as the Laplace transform, with argument x, of the function e^{-1/2t^2.

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 ...