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


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.


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