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Variations on a theme – Euler and the logsine integral

Published online by Cambridge University Press:  23 January 2015

Nick Lord
Nick Lord*
Affiliation:
Tonbridge School, Kent TN9 1JP
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Extract

This article concerns the evaluation of the ‘logsine’ integral

We shall encounter it in several guises. Indeed, standard integration techniques used below readily show that (1) has the same value as the following integrals:

En passant, it is worth noting that forms (6) and (7) are the best behaved for numerical integration.

I first met the logsine integral as a callow youth in that strange hinterland of results that you may not have met at school but were not guaranteed to meet later on either.

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Type
Articles
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The Mathematical Gazette , Volume 96 , Issue 537 , November 2012 , pp. 451 - 458
Copyright
Copyright © The Mathematical Association 2012

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