Analytic continuation of Riemann’s zeta function and values at negative integers via Euler’s transformation of series
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- by Jonathan Sondow PDF
- Proc. Amer. Math. Soc. 120 (1994), 421-424 Request permission
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.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- 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