Rothe–Hagen identity explained

In mathematics, the Rothe–Hagen identity is a mathematical identity valid for all complex numbers (

x, y, z ) except where its denominators vanish:\sum ^{n (x)/(x + kz)} _{k =0} {x + kz \choose k} (y)/(y + (n - k)z) {y + (n - k)z \choose n - k} = (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.

References

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