I found an old Macsyma notebook equating the area enclosed by Koch's Snowflake (easy geometric sum) with the area enclosed by my(?) Fourier series for it, using A = π Sum n |c_n|^2. (Which, apparently, not everybody knows: http://www.mathworks.com/matlabcentral/answers/52325-2d-integration-over-an-... ) I probably sent this before: Sum[Product[1 - Tan[((k + 1/2)*π)/(-2)^n], {n,∞}]^2/(k + 1/2)^3, {k, -∞,∞}] ==π^3/2 But I don't remember the enormous difficulty in numerically testing it that I now encounter. After a couple of million terms, most are negligible, but those with k of the form, e.g., (-2 - (-2)^j)/3, j>0, are not. But adding these in for 22<j<99 still gives me < two significant figures! Presumably, there are other families of non-negligible k. This is annoying. I have the expansion for "Snowflakes" of any dimension ≤ 2, and was hoping to watch what happens to the enclosed area as the dimension approaches 2 and the order of approximation approaches ∞, and the enclosed area is suddenly all boundary. --rwg