I don't think (1/1-x) is summable by any means at x=1, let alone 1/(1-x)^2, whereas there's no pole at zeta(-1). On Fri, Oct 6, 2017 at 1:22 PM, <rcs@xmission.com> wrote:
.5 Grumble.
Write 1/(1-x)^2 = 1 + 2x + 3x^2 + 4x^3 + ... Substitute x = 1 to get 1/infinity^2, a double pole. Why choose zeta, rather than a simple rational function, to do your extrapolation?
Rich
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Quoting Mike Stay <metaweta@gmail.com>:
Summing up the naturals gives infinity, but you can analytically continue the Riemann zeta function to -1 and get -1/12. Here's the story about bosonic string theory: http://math.ucr.edu/home/baez/numbers/24.pdf
On Fri, Oct 6, 2017 at 11:39 AM, Guy Haworth <g.haworth@reading.ac.uk> wrote:
For some reason, this maths-chat turned up on the Chessbase site ... http://en.chessbase.com/post/a-math-break
Someone, please tell me that some formula is being used outside its 'zone of convergence' ... and that 'String Theory' is not using dodgy arithmetic.
Thanks in advance,
Guy
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