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Gradshteĭn, I.S., Zwillinger, D. and Ryzhik, I.M. (2015) Table of Integrals, Series and Products. Editor: Moll, V.H., 8th Edition, Massachusetts Academic Press, eBook, Waltham, 30-31.

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• 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.