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arXiv · 2208.02624

New series representations for any positive power of $\pi$ from a relation involving trigonometric functions

Jean-Christophe Pain
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Abstract

In previous works, we presented series representations for $\pi^3$ and $\pi^5$, in which the prefactor depends only on the golden ratio appears. In this article, we derive a general relation involving trigonometric functions and an infinite series. Such an identity is likely to provide many series representations for any positive power of $\pi$, among them the above mentioned representations for $\pi^3$ and $\pi^5$.

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Jean-Christophe Pain. 2022-07-27. New series representations for any positive power of $\pi$ from a relation involving trigonometric functions. https://arxiv.org/abs/2208.02624

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