$$\text{beta}\left(a,b\right)={\left(\frac{a+g-0.5}{a+b+g-0.5}\right)}^{a-0.5}{\left(\frac{b+g-0.5}{a+b+g-0.5}\right)}^b\sqrt{\frac{e}{b+g-0.5}}\frac{L\left(a\right)L\left(b\right)}{L\left(c\right)}$$