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Integrals evaluated in terms of Catalan's constant

Published online by Cambridge University Press:  03 February 2017

Graham Jameson
Affiliation:
Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF e-mail: [email protected]
Nick Lord
Affiliation:
Tonbridge School, Tonbridge, Kent TN9 1JP e-mail: [email protected]

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
Copyright
Copyright © Mathematical Association 2017 

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References

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