Trigonometric Identities à la Hermite
Author: Johnson, Warren P.
Source: American Mathematical Monthly, Volume 117, Number 4, April 2010 , pp. 311-327(17)
Publisher: Mathematical Association of America
Abstract:Hermite once observed that a certain product of cotangents can be integrated by breaking it into a sum of cotangents, where the coefficients are themselves products of cotangents. Why should such an identity exist? We give two derivations, one based on the partial fractions expansion of the cotangent. Hermite seems to have used a mixture of the two. We also discuss and extend a second theorem of Hermite, which leads to generalizations of his cotangent identity. The paper veers off into determinants at the end.
Document Type: Research Article
Publication date: April 2010
- American Mathematical Monthly publishes articles, notes, and other features about mathematics and the profession. AMM readers span a broad spectrum of mathematical interests, and include professional mathematicians as well as students of mathematics at all collegiate levels.
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