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Analytic continuation of Riemann's zeta function and values at negative integers via Euler's transformation of series


Author: Jonathan Sondow
Journal: Proc. Amer. Math. Soc. 120 (1994), 421-424
MSC: Primary 11M06
DOI: https://doi.org/10.1090/S0002-9939-1994-1172954-7
MathSciNet review: 1172954
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Abstract: We prove that a series derived using Euler's transformation provides the analytic continuation of $ \zeta (s)$ for all complex $ s \ne 1$. At negative integers the series becomes a finite sum whose value is given by an explicit formula for Bernoulli numbers.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1172954-7
Article copyright: © Copyright 1994 American Mathematical Society

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