We denote by $\tilde{h}$ the restriction of the function $h : ]0,1[ \longrightarrow \mathbf{R},\; t \longmapsto \frac{1}{\sqrt{t(1-t)}}$ to the interval $\left]0, \frac{1}{2}\right]$. Verify that the function $\tilde{h}$ is decreasing on $]0, \frac{1}{2}[$, then show that the function $\tilde{h}$ belongs to $\mathscr{D}_{0, \frac{1}{2}}$.