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      Instant Evaluation and Demystification of zeta(n),L(n,chi) that Euler,Ramanujan Missed III

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          Abstract

          We show that for a non-positive value of the first variable,Hurwitz zeta function becomes a polynomial in the second variable. We show this, using 'integration approach', instead of 'power series approach', which we had resorted to, in our earlier paper with the same title. This, in particular, explains why Riemann zeta function at positive even integer arguments, can be evaluated and why it cannot be evaluated explicitly at positive odd integer arguments.

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          Author and article information

          Journal
          20 July 2008
          Article
          0807.3148
          664b2507-095e-4ffe-8edd-a9ce9670df87

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          11M35
          9 Pages
          math.NT

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