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Remarkable matrices and trigonometric identities

✍ Scribed by F. Calogero


Book ID
104338466
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
191 KB
Volume
83
Category
Article
ISSN
0377-0427

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✦ Synopsis


Two (n x n)-matrices are exhibited, which have a simple expression in terms of trigonometric functions of n arbitrary angles and possess remarkably neat spectral properties, such as integral eigenvalues. Several related trigonometric identities are also exhibited.


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Trigonometric summations over the angles equally divided on the upper half plane are investigated systematically. Their generating functions are established by expansions of trigonometric polynomials in partial fractions. The explicit formulas are displayed and their proofs are presented in brief th