In a previous post I was told to use RealField if I wanted very high
degrees of accuracy.

I'm still now sure I'm using RealField right and would appreciate any
help debugging my puzzle.

sage: constant = 100*sqrt(pi/log(10.0))
sage: f(k) = 10^(-k^2/10000.0)
sage: N = 10000
sage: RealField(100000)(sum(f(k) for k in range(-N, N))- constant)

The infinite sum should agree with the constant to over 18000 digits.
As I increase the value of N and the size of the mantissa  I can't
seem to ever get more than around 13 digits of agreement.

(Context can be found at top of page 2 of this paper:
http://arxiv.org/abs/math.GM/0409014/ )

Sincerely,

Chris

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