Re: [PrimeNumbers] Euler's Zeta function equality and the Fall from Infinity
- In a message dated 05/06/03 06:26:35 GMT Daylight Time, marku606@...
> It strains my brains that the sum could fall from infinite to finiteWhy so?
> with (I presume) an infinitely small increment of the n exponent.
tan(theta) falls from infinite to finite for an infinitely small increment of
theta from pi/2...
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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;