$$e^{x-a}{\left(\frac{x}{a+g-0.5}\right)}^a=e^{\left(a\text{log1pmx}\left(\frac{x-a-g+0.5}{a+g-0.5}\right)+\frac{x\left(0.5-g\right)}{a+g-0.5}\right)};\text{log1pmx}\left(z\right)=\ln \left(1+z\right)-z$$