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An interesting family of cosine integrals

Published online by Cambridge University Press:  15 October 2025

David Hopkins
David Hopkins*
Affiliation:
27 Byron Mews, London NW3 2NQ e-mail: david.k.hopkins@blueyonder.co.uk
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Extract

In a previous article [1] I showed that the probability of a difference of t units arising when n numbers from a uniform distribution are rounded before, as opposed to after, they are added is(1)Here n is a non-negative integer and t is a positive or negative integer with, the maximum possible error.

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Type
Articles
Information
The Mathematical Gazette , Volume 109 , Issue 576 , November 2025 , pp. 449 - 461
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© The Authors, 2025 Published by Cambridge University Press on behalf of The Mathematical Association

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References

Hopkins, David, Will my numbers add up correctly if I round them?, Math. Gaz. 100 (November 2016) pp. 396–409.10.1017/mag.2016.104CrossRefGoogle Scholar
Ruiz, Sebastián Martin, An algebraic identity leading to Wilson’s theorem, Math. Gaz. 80 (November 1996) pp. 579–582.10.2307/3618534CrossRefGoogle Scholar
Trainin, J., Integrating expressions of the form and others, Math. Gaz. 94 (July 2010) p. 222.10.1017/S0025557200006471CrossRefGoogle Scholar
Nahin, Paul J., Inside interesting integrals, Springer (2015), Section 3.3.10.1017/mag.2025.10125 10.1007/978-1-4939-1277-3CrossRefGoogle Scholar