How would you understand in a intuitive way the meaning of: $$D^{\frac{1}{2}}x^2=\frac{\Gamma(3)}{\Gamma(\frac{5}{2})}x^{\frac{3}{2}}=\frac{8}{3\sqrt{\pi}}x^{\frac{3}{2}}$$
or $$D^{\frac{1}{2}}x=\frac{\Gamma(2)}{\Gamma(\frac{1}{2})}x^{\frac{1}{2}}=\frac{2}{\sqrt{\pi}}x^{\frac{1}{2}}$$
