Functions and Analysis


Integrals Containing the Infinite Product $\prod_{n=0}^\infty\left[1+\left(\frac{x}{b+n}\right)^3\right]$

Authors: Martin Nicholson

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.

Comments: 8 Pages.

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Submission history

[v1] 2017-12-20 06:47:39

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