# Sinc integrals and tiny numbers

@article{Basel2015SincIA,
title={Sinc integrals and tiny numbers},
author={Uwe Basel and Robert Baillie},
journal={Elemente Der Mathematik},
year={2015},
volume={71},
pages={7-20}
}
• Published 12 October 2015
• Mathematics
• Elemente Der Mathematik
We apply a result of David and Jon Borwein to evaluate a sequence of highly-oscillatory integrals whose integrands are the products of a rapidly growing number of sinc functions. The value of each integral is given in the form $\pi(1-t)/2$, where the numbers $t$ quickly become very tiny. Using the Euler-Maclaurin summation formula, we calculate these numbers to high precision. For example, the integrand of the tenth integral in the sequence is the product of 68100152 sinc functions. The…
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