# Gamma Triplication formula using Beta Function

Recently i have seen that you can develope the Legendre Duplication Formula by using Beta FUnction.

http://mathworld.wolfram.com/LegendreDuplicationFormula.html

And i´m interesting to develope the triplication formula also using Beta Function.

$$\Gamma (3z)=(2 \pi)^{-1}3^{3z-1/2}\Gamma(z)\Gamma \left(z+\frac{1}{3}\right)\Gamma\left(z+\frac{2}{3}\right)$$

But i don´t see how to do ot, since in the article they use $m=n=z$ wich gives inmediatly $2z$ in the denominator.

• My advice would be to split $(3n)!$ into three subproducts, depending on the remainder each term leaves when divided by $3$. – Lucian Sep 29 '15 at 14:02
• – cgiovanardi Sep 19 '16 at 21:03