Supposedly the answer is 1 but I have no idea how to evaluate this thing analytically.


$$f(n) = \frac{2}{\pi} \int\_{0}^{\infty} 2\cos(x) \cdot \frac{\sin(x)}{x} \cdot \frac{\sin(x/3)}{x/3} \cdot \cdots \cdot \frac{\sin(x/(2n+1))}{x/(2n+1)} dx$$


Any help would be appreciated.



Evaluation of an interesting Integral
The conjecture $f(n)=1$ is only correct for $n\leq 55$, see H. Schmid, [Two curious integrals and a graphic proof](http://www.schmid-werren.ch/hanspeter/publications/2014elemath.pdf). For $n=56$ an analytical calculation using the Poisson summation formula gives
$$f(56)= 1 − 1.484870809 \cdot 10^{−138},$$
see [More remarkable sinc integrals and sums](https://arxiv.org/abs/1405.1265). 


Schmid remarks:



> 
> When this [deviation from unity] was recently verified by a researcher using a computer
>  algebra package, he concluded that there must be a “bug” in the
>  software. It is not a bug, though; this series of integrals really
>  only results in 1 up to a certain point, and then breaks down. This
>  astonishes most mathematically educated readers...
> 
> 
> 


