$$\text{gp1m1}\left(z\right)=\sqrt{1+\frac{z}{g+0.5}}\left([{\left(\frac{z+g-0.5}{e}\right)}^z-1]+[L\left(z\right)-1]{\left(\frac{z+g-0.5}{e}\right)}^z\right)+[\sqrt{1+\frac{z}{g+0.5}}-1]$$