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arXiv · 1712.07456

Integrals containing the infinite product $\prod_{n=0}^\infty\Bigl[1+\bigl(\frac{x}{b+n}\bigr)^3\Bigr]$

Martin Nicholson
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Abstract

We study several integrals that contain the infinite product ${\displaystyle\prod_{n=0}^\infty}\left[1+\left(\frac{x}{b+n}\right)^3\right]$ in the denominator of their integrand. These considerations lead to closed form evaluation $\displaystyle\int_{-\infty}^\infty\frac{dx}{\left(e^x+e^{-x}+e^{ix\sqrt{3}}\right)^2}=\frac{1}{3}$ and to some other formulas.

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Martin Nicholson. 2017-12-20. Integrals containing the infinite product $\prod_{n=0}^\infty\Bigl[1+\bigl(\frac{x}{b+n}\bigr)^3\Bigr]$. https://arxiv.org/abs/1712.07456

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