convergence of Riemann zeta series
Proof. Let where and are real numbers and . Then
Since the series converges, by the -test (http://planetmath.org/PTest), for , we conclude that the series (1) is absolutely convergent in the half-plane .
Title | convergence of Riemann zeta series |
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Canonical name | ConvergenceOfRiemannZetaSeries |
Date of creation | 2015-08-22 13:15:14 |
Last modified on | 2015-08-22 13:15:14 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 8 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 11M06 |
Classification | msc 30A99 |
Related topic | ModulusOfComplexNumber |
Related topic | ComplexExponentialFunction |