## Infinite Tetration of Euler’s Number and the Z-Exponential

**Authors:** C. A. Laforet

It is shown that the infinite tetration of Euler’s number is equal to any complex number. It is also found that starting with any complex number except 0 and 1, we can convert the complex number into an exponential with a complex exponent. If this is done recursively for each successive exponent, we find that the complex exponent converges to a constant number, which is named the Z-Exponential (Z_e). Derivatives for the Z-Exponential function are derived as well as its relationship to the exponential and natural logarithm.

**Comments:** 3 Pages.

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### Submission history

[v1] 2017-02-06 11:01:59

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