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Re: [PrimeNumbers] Euler's Zeta function equality and the Fall from Infinity

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  • mikeoakes2@aol.com
    In a message dated 05/06/03 06:26:35 GMT Daylight Time, marku606@yahoo.ca ... Why so? tan(theta) falls from infinite to finite for an infinitely small
    Message 1 of 4 , Jun 5, 2003
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      In a message dated 05/06/03 06:26:35 GMT Daylight Time, marku606@...
      writes:


      > It strains my brains that the sum could fall from infinite to finite
      > with (I presume) an infinitely small increment of the n exponent.
      >

      Why so?
      tan(theta) falls from infinite to finite for an infinitely small increment of
      theta from pi/2...

      Mike Oakes


      [Non-text portions of this message have been removed]
    • Jon Perry
      It strains my brains that the sum could fall from infinite to finite ... Infinitely or finitely? Consider 1/e. As e- 0 the expression has a value, at e=0 it
      Message 2 of 4 , Jun 5, 2003
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        '> It strains my brains that the sum could fall from infinite to finite
        > with (I presume) an infinitely small increment of the n exponent.
        > '

        Infinitely or finitely?

        Consider 1/e. As e->0 the expression has a value, at e=0 it is undefined.
        This is basic continuity theory.

        The behaviour of zeta(s) around s=1 is analysed at;

        http://numbers.computation.free.fr/Constants/Miscellaneous/zeta.html

        Jon Perry
        perry@...
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