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91.20 Finding ζ(2n) from a recursion relation for Bernoulli numbers

Published online by Cambridge University Press:  01 August 2016

Thomas J. Osler
Affiliation:
Mathematics Department, Rowan University, Glassboro, NJ 08028, USAe-mail: [email protected]
Jim Zeng
Affiliation:
Mathematics Department, Rowan University, Glassboro, NJ 08028, USAe-mail: [email protected]

Abstract

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Type
Notes
Copyright
Copyright © The Mathematical Association 2007

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References

1. Apostol, Tom M., Another elementary proof of Euler’s formula for ζ (2n), Amer. Math. Monthly, 80 (1973) pp. 425431.Google Scholar
2. Ayoub, Raymond, Euler and the zeta function, Amer. Math. Monthly, 81 (1974) pp. 10671086.Google Scholar
3. Berndt, Bruce C., Elementary evaluation of ζ (n), Mathematics Magazine, 48 (1975) pp. 148154.Google Scholar
4. Edwards, H. M.,Riemann’s zeta function, Academic Press, New York (1974).Google Scholar
5. Euler, Leonard, Introduction to analysis of the infinite, Book I, (Translated by Blanton, John D.) Springer-Verlag, New York (1988) pp. 137153.Google Scholar
6. Knopp, Konrad, Theory and application of infinite series, Dover Publications, New York (1990) pp. 236240. (A translation by Young, R. C. H. of the 4th German addition of 1947.)Google Scholar
7. Osier, Thomas J., Finding zeta(2p) from a product of sines. Amer. Math. Monthly, 111 (2004) pp. 5254.Google Scholar
8. Williams, Kenneth S., On , Mathematics Magazine, 44 (1971) pp. 273276.Google Scholar
9. Titchmarsh, E. C. and Heath-Brown, D. R., The theory of the Riemann zeta-function, (2nd ed.), Oxford University Press (1986).Google Scholar