Dirichlet eta function
For , the Dirichlet eta function is defined as
(1) |
Let . For a positive real number the series converges by the alternating series test, by the second listed in the entry on Dirichlet series it converges for all with .
It can be shown that , where is the Riemann zeta function. The pole of at is cancelled by the zero of .
Title | Dirichlet eta function |
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Canonical name | DirichletEtaFunction |
Date of creation | 2013-03-22 14:31:28 |
Last modified on | 2013-03-22 14:31:28 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 9 |
Author | Mathprof (13753) |
Entry type | Definition |
Classification | msc 11M41 |
Related topic | ZerosOfDirichletEtaFunction |