$$\psi \left(x\right)=\frac{z-\frac{1}{2}}{x+g-\frac{1}{2}}+\ln \left(x+g-\frac{1}{2}\right)+\frac{P^{\prime }\left(x\right)}{P\left(x\right)}-\frac{Q^{\prime }\left(x\right)}{Q\left(x\right)}-1$$