mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, the Rothe–Hagen identity is a

mathematical identity In mathematics, an identity is an equality relating one mathematical expression ''A'' to another mathematical expression ''B'', such that ''A'' and ''B'' (which might contain some variables) produce the same value for all values of ...

valid for all

complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...

s (

x, y, z

) except where its denominators vanish: :

\sum_^n\frac\frac=\frac.

It is a generalization of

Vandermonde's identity In combinatorics, Vandermonde's identity (or Vandermonde's convolution) is the following identity for binomial coefficients: :=\sum_^r for any nonnegative integers ''r'', ''m'', ''n''. The identity is named after Alexandre-Théophile Vandermon ...

, and is named after

Heinrich August Rothe Heinrich August Rothe (1773–1842) was a German mathematician, a professor of mathematics at Erlangen. He was a student of Carl Hindenburg and a member of Hindenburg's school of combinatorics. Biography Rothe was born in 1773 in Dresden, and in ...

and

Johann Georg Hagen Johann (John) Georg Hagen (March 6, 1847 – September 6, 1930) was an Austrian Society of Jesus, Jesuit priest and astronomer. After serving as Director of the Georgetown University Astronomical Observatory, Georgetown University Observator ...

References

*. *. See especially pp. 89–91. *. As cited by . *. *. As cited by . Factorial and binomial topics Algebraic identities Complex analysis {{mathapplied-stub