Researchers thought this was a bug (Borwein integrals)

Summary by Krater

This video explores why certain products of sinc function integrals evaluate to pi, using moving averages and Fourier transforms to explain the phenomenon.

From the video

Answers: Why do certain products of sinc function integrals evaluate to pi before abruptly breaking?

• sinc function integrals
• Fourier transforms
• convolution theorem
• moving averages
• rect function

What it concludes

• Products of sinc function integrals equal pi when the sum of their factors is less than 1.
• The evaluation of sinc integrals can be interpreted through moving averages of a rectangular function.
• The convolution theorem relates multiplication of functions in one domain to convolution in the Fourier transform domain.