“Hermite's cotangent identity”的意思、由来-开放百科全书

词条

Hermite's cotangent identity

释义

Notes and references

{{distinguish|text=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, ..., a_n are complex numbers, no two of which differ by an integer multiple of {{pi}}. Let

(in particular, A_1,1, being an empty product, is 1). Then

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

Notes and references

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

1 : Trigonometry

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