= Inverse-square-root singularity
{title2=$f(x)\sim C(x-x_0)^{-1/2}$}
An endpoint <integrable singularity> with $f(x)\sim C/\sqrt{x-x_0}$ as $x\downarrow x_0$, for finite nonzero $C$. It is an <integrable singularity> because $\int_{x_0}^{x_0+\epsilon}(x-x_0)^{-1/2}\,dx=2\sqrt\epsilon$. One common origin is a stationary <change of variables>: if $y-y_0=bz^2+O(z^4)$ with $b>0$ and a smooth nonzero <probability density> for $z$ at zero, the two inverse branches give a <probability density> for $y$ proportional to $(y-y_0)^{-1/2}$.
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