\[\frac{3\pi(8n+5)}{9+8\xi_{n}}\xi_{n}^{3/2}=\dfrac{27}{16}\left(\dfrac{3}{2}%
\right)^{1/2}\left(\ln\left(\frac{1}{\xi_{n}}\right)+3\ln\left(\dfrac{3}{2}%
\right)\right).\]