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Integrals evaluated in terms of Catalan's constant

Published online by Cambridge University Press:  03 February 2017

Graham Jameson  and
Nick Lord
Graham Jameson
Affiliation:
Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF e-mail: g.jameson@lancaster.ac.uk
Nick Lord
Affiliation:
Tonbridge School, Tonbridge, Kent TN9 1JP e-mail: njl@tonbridge-school.org
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Extract

Catalan's constant, named after E. C. Catalan (1814-1894) and usually denoted by G, is defined by

It is, of course, a close relative of

The numerical value is G ≈ 0.9159656. It is not known whether G is irrational: this remains a stubbornly unsolved problem. The best hope for a solution might appear to be the method of Beukers [1] to prove the irrationality of ζ (2) directly from the series, but it is not clear how to adapt this method to G.

Type
Articles
Information
The Mathematical Gazette , Volume 101 , Issue 550 , March 2017 , pp. 38 - 49
Copyright
Copyright © Mathematical Association 2017 

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References

1. Beukers, F., A note on the irrationality of ζ (2) and ζ (3), Bull. London Math. Soc. 11 (1979) pp. 268–272.Google Scholar
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9. Jameson, G. J. O., Elliptic integrals, the arithmetic-geometric mean and the Brent-Salamin algorithm for π, accessed October 2016 at http://www.maths.lancs.ac.uk/~jameson Google Scholar
10. Lord, Nick, Evaluating integrals using polar areas, Math. Gaz. 96 (July 2012), pp. 289–296.Google Scholar