my-server
← Wiki

Hermite's cotangent identity

In mathematics, Hermite's cotangent identity is a trigonometric identity discovered by Charles Hermite. Suppose a<sub>1</sub>,&nbsp;...,&nbsp;a<sub>n</sub> are complex numbers, no two of which differ by an integer multiple of&nbsp;. Let

(in particular, A<sub>1,1</sub>, being an empty product, is&nbsp;1). Then

The simplest non-trivial example is the case&nbsp;n&nbsp;=&nbsp;2:

Notes and references