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Walker's Equation

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  • Jon Perry
    Anyone seen this before? http://www.geocities.com/aj_thomas_w/WalkerEquation.html Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry
    Message 1 of 3 , Feb 2, 2002
    • djbroadhurst
      Eq(22) at http://mathworld.wolfram.com/RiemannZetaFunction.html
      Message 2 of 3 , Feb 2, 2002
      • djbroadhurst
        PS: The proof is elementary sum_{n 1,m 1} 1/n^m = sum_{n 1} 1/(n*(n-1)) = sum_{n 1} (1/(n-1) - 1/n) = 1/(2-1) = 1 Numerical check: ? p60 realprecision = 67
        Message 3 of 3 , Feb 2, 2002
          PS: The proof is elementary

          sum_{n>1,m>1} 1/n^m = sum_{n>1} 1/(n*(n-1))
          = sum_{n>1} (1/(n-1) - 1/n) = 1/(2-1) = 1

          Numerical check:

          ? \p60
          realprecision = 67 significant digits (60 digits displayed)
          ? print(suminf(n=2,zeta(n)-1))
          1.00000000000000000000000000000000000000000000000000000000000
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