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Sinc integrals and tiny numbers

Uwe Bäsel, Robert Baillie

2016
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Elemente der Mathematik
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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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... ctions. The corresponding $t$ is approximately $9.6492736004286844634795531209398105309232 \cdot 10^{-554381308}$.

doi:10.4171/em/295
fatcat:s6ftb7x3bffsrilczw3kc2espm