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# 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:

$sum_\left\{k=0\right\}^nfrac\left\{x\right\}\left\{x+kz\right\}\left\{x+kz choose k\right\}frac\left\{y\right\}\left\{y+\left(n-k\right)z\right\}\left\{y+\left(n-k\right)z choose n-k\right\}=frac\left\{x+y\right\}\left\{x+y+nz\right\}\left\{x+y+nz choose n\right\}.$

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