Referring to equation (10.5.31) for the phase shifts \(\eta_{l}(k)\) of a hard-sphere gas, show that for \(k D \ll 1\)

\[\eta_{l}(k) \simeq-\frac{(k D)^{2 l+1}}{(2 l+1)\{1 \cdot 3 \cdots(2 l-1)\}^{2}}\]