"game" - to calculate 1.00...001 ^^ 0.5 = ?

[andydude]

it's correct!??? no.

Sorry about that, that code calculates \( {}^{y}(c^{1/c}) \). So, you input the wrong value. 'c' is the fixed point, not the base. In order to calculate base 1.00000000000000000001 tetration you must use

Code:

H[x_] := -ProductLog[-Log[x]]/Log[x];
base = 1.00000000000000000001`500;
tet = c + Normal[RegularIterate[Series[c^((x + c)/c) - c, {x, 0, 10}], y]]/.x->(1-c);
tet /. {c -> H[base], y -> 0.5`500}

Hope that helps.

Andrew Robbins