psix=begincases frac1+sqrt34quad0leq xfrac12-fracsqrt34 frac3+sqrt34quadfrac12-fracsqrt34leq xfrac12+fracsqrt34 frac3-sqrt34quadfrac12+fracsqrt34leq x1-fracsqrt34 frac1-sqrt34quad1-fracsqrt34leq x1 0q

$$ \psi(x)=\begin{cases} \frac{1+\sqrt{3}}{4} & 0\leq x<\frac{1}{2}-\frac{\sqrt{3}}{4}\ \frac{3+\sqrt{3}}{4} & \frac{1}{2}-\frac{\sqrt{3}}{4}\leq x<\frac{1}{2}+\frac{\sqrt{3}}{4}\ \frac{3-\sqrt{3}}{4} & \frac{1}{2}+\frac{\sqrt{3}}{4}\leq x<1-\frac{\sqrt{3}}{4}\ \frac{1-\sqrt{3}}{4} & 1-\frac{\sqrt{3}}{4}\leq x<1\ 0 & \text{otherwise} \end{cases} $$