TITLE:
Generalized Trigonometric Power Sums Covering the Full Circle
AUTHORS:
Hans Jelitto
KEYWORDS:
Trigonometric Power Sum, Power Reduction Formula, Trigonometric Identity, Central Binomial Coefficient
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.2,
February
21,
2022
ABSTRACT: The analytical calculation of the area moments of inertia used for special mechanical tests in materials science and further generalizations for moments of different orders and broader symmetry properties has led to a new type of trigonometric power sums. The corresponding generalized equations are presented, proven, and their characteristics discussed. Although the power sums have a basic form, their results have quite different properties, dependent on the values of the free parameters used. From these equations, a large variety of power reduction formulas can be derived. This is shown by some examples.