\[{\theta_{\nu}'}^{2}\left(x\right)+\frac{1}{2}\frac{\theta_{\nu}'''\left(x%
\right)}{\theta_{\nu}'\left(x\right)}-\frac{3}{4}\left(\frac{\theta_{\nu}''%
\left(x\right)}{\theta_{\nu}'\left(x\right)}\right)^{2}=1-\frac{\nu^{2}-\tfrac%
{1}{4}}{x^{2}}.\]