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Series involving ζ(n)

Published online by Cambridge University Press:  23 January 2015

G.J.O. Jameson
G.J.O. Jameson*
Affiliation:
Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF e-mail: g.jameson@lancaster.ac.uk
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Extract

Recall that for integers n ≥ 2, ζ (n) is defined by

Of course, ζ (1) is not defined, since is divergent. A well-known particular value is ζ (2) = π2/6: numerous alternative proofs of this fact have been presented in the Gazette, e.g. the recent notes [1], [2].

Type
Articles
Information
The Mathematical Gazette , Volume 98 , Issue 541 , March 2014 , pp. 58 - 66
Copyright
Copyright © The Mathematical Association 2014

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References

1. Jameson, G.J.O. and Lord, Nick, Evaluation of by a double integral, Math. Gaz. 97 (November 2013) pp. 504–505.CrossRefGoogle Scholar
2. Jameson, T.P., Another proof that ζ (2) = π2/6 by double integration, Math. Gaz. 97 (November 2013) pp. 506–507.CrossRefGoogle Scholar
3. Lord, Nick, Intriguing integrals: an Euler-inspired odyssey, Math. Gaz. 91 (November 2007) pp. 415–427.CrossRefGoogle Scholar
4. Douglass, Steven A., Introduction to mathematical analysis, Addison-Wesley (1996).Google Scholar
5. Whittaker, E.T. and Watson, G.N., A course of modern analysis Cambridge University Press (1927).Google Scholar
6. Abramowitz, Milton and Stegun, Irene A., Handbook of mathematical functions, Dover, New York (1965).Google Scholar