Rothe–Hagen identity

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


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

It is a generalization of Vandermonde's identity, and is named after Heinrich August Rothe and Johann Georg Hagen.