Trigonometric identities
type: Item
instance of: scholarly article
title: Trigonometric identities
zbMATH Open document ID: 0612.12008
DOI: 10.1155/S0161171286000844
author: Malvina Baica
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46145
review text: Der Verf. folgert die Identität \[ 2^{(n-1)(n-2)/2}\prod^{n- 2}_{k=1}(1-\cos (2\pi k/n))^{n-1-k}=n^{n-2} \] für alle ganzen \(n\geq 3\) aus der Darstellung \(| V^ 2| =n^ n\) der Vandermondeschen Determinante \(V=\det (e^{2\pi i k\ell /n})_{0\leq k,\ell <n}\) und führt sie außerdem in den Fällen \(n=5,7\) auf trigonometrische Identitäten zurück, die schon C. F. Gauß angegeben hatte.
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 12E12
Mathematics Subject Classification ID: 11L99
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 3989483
zbMATH Keywords: trigonometric identities
zbMATH Keywords: cyclotomic field
reviewed by: Wolfgang Haneke
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3989483