$$\mathrm{\text{ CF2}}:p+iq=\frac{J_{\nu }^{\prime }+i{Y}_{\nu }^{\prime }}{J_{\nu }+i{Y}_{\nu }}=\left(i-\frac{1}{2x}\right)+\frac{i}{x}\left[\frac{{\left(\frac{1}{2}\right)}^2-{\nu }^2}{2\left(x+i\right)+}\frac{{\left(\frac{3}{2}\right)}^2-{\nu }^2}{2\left(x+2i\right)+}\cdot \cdot \cdot \right]$$