Rothe–Hagen identity

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

$\sum _{k=0}^n\frac{x}{x+kz}(\genfrac{}{}{0ex}{}{x+kz}{k})\frac{y}{y+(n-k)z}(\genfrac{}{}{0ex}{}{y+(n-k)z}{n-k})=\frac{x+y}{x+y+nz}(\genfrac{}{}{0ex}{}{x+y+nz}{n}).$

It is a generalization of Vandermonde's identity, and is named after the independent work of Heinrich August Rothe in 1793 and of Johann Georg Hagen in 1891.

References

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