Rothe-Hagen identity

In mathematics, the Rothe-Hagen identity is a mathematical identity valid for all complex numbers ($x,\; y,\; z$) except where the denominators vanish:

:$sum\_\{k=0\}^nfrac\{x\}\{x+kz\}\{x+kz\; choose\; k\}frac\{y\}\{y+(n-k)z\}\{y+(n-k)z\; choose\; n-k\}=frac\{x+y\}\{x+y+nz\}\{x+y+nz\; choose\; n\}.$