Beta Function of x with y+m+1

Theorem
Let $\map \Beta {x, y}$ denote the Beta function.

Then:
 * $\map \Beta {x, y} = \dfrac {\map {\Gamma_m} y m^x} {\map {\Gamma_m} {x + y} } \map \Beta {x, y + m + 1}$

where $\Gamma_m$ is the partial Gamma function: