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.
Ptolemy's Theorem and Familiar Trigonometric Identities
β Scribed by James K. Bidwell
- Book ID
- 114978903
- Publisher
- School Science and Mathematics Association
- Year
- 1993
- Tongue
- English
- Weight
- 203 KB
- Volume
- 93
- Category
- Article
- ISSN
- 0036-6803
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
Asgeirsson's mean value theorem states that if u satisfies the ultrahyperbolic differential equation (2 We extend this to solutions of the inhomogeneous equation by proving that f =(2 x &2 y ) + R where + on R are defined by / a + (t)=t a + Γ1(a+1) when Re a>&1 and then continued analytically to a