Hermite's cotangent identity

From Wikipedia, the free encyclopedia
Jump to: navigation, search
Not to be confused with Hermite's identity, a statement about fractional parts of integer multiples of real numbers.

In mathematics, Hermite's cotangent identity is a trigonometric identity discovered by Charles Hermite.[1] Suppose a1, ..., an are complex numbers, no two of which differ by an integer multiple of π. Let

(in particular, A1,1, being an empty product, is 1). Then

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

Notes and references[edit]

  1. ^ Warren P. Johnson, "Trigonometric Identities à la Hermite", American Mathematical Monthly, volume 117, number 4, April 2010, pages 311–327