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Tables of Values

Here are tables of values for tetration using the bases 2, e, and 10. These tables were auto-generated using a 5th approximation of tetration, so only 3-4 digits are accurate.

And here is a full representation of 52:

About  πe

The value of πe is one of the questions that started this investigation. It would be fitting, then, to focus on this one value now that an infinitely differentiable extension has been found. Here is a summary of what is known to be exact, using the approximations described in my paper:

The reason for these values can be seen in the values of successive approximations of the inverse super-logarithm, as defined in my paper. An exact value in this context, is defined to be the digits within the decimal representation of the values of the n-th approximation and 2n-th approximation for the same input, that agree when rounded to the nearest place value that would allow agreement. The rounding system used here, however is subjective, a 5 can either be rounded up or down, other than that normal half-rounding is used:

Visited: times, last updated: 2006-02-15, by: Andrew Robbins, contact: and_j_rob(at)yahoo(dot)com