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Novel constant

  1. Dec 28, 2008 #1
    [tex] \sum _{s =1}^{\infty}s^{-s}= ? [/tex]

    [tex] \int _{1}^{\infty}s^{-s}ds= ? [/tex]

    Does either this summation or integral define a fundamental constant?
  2. jcsd
  3. Dec 29, 2008 #2


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    The sum is 1.291285997062663540407282590595600541498619368274..., Sloane's A073009.

    The integral is 1.99545595750013800041872469845272435208621663... Both sum and integral are easy to calculate to a large number of decimal places.

    The integral over 0 to 1 has the same value as the sum. I wasn't able to find anything interesting about the integral from 1 to infinity.
  4. Dec 29, 2008 #3
    Thank you for your research, CR. I guess they have no direct derivation from the constant e.
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