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arXiv · 2206.15281

Series representations for $\pi^3$ involving the golden ratio

Jean-Christophe Pain
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Abstract

Although many series exist for $\pi$ and $\pi^2$, very few are known for $\pi^3$. In this article, we derive, using a trigonometric identity obtained by Euler, two representations of $\pi^3$ involving infinite sums and the golden ratio. The methodology can be generalized in order to obtain further series, relating by the way $\pi^3$ to other mathematical constants.

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Jean-Christophe Pain. 2022-06-30. Series representations for $\pi^3$ involving the golden ratio. https://arxiv.org/abs/2206.15281

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