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Should tetration be a multivalued function?
@marraco, @tommy
That certainly is a cool equation, even if it is easily provable.

Also, I think I can express my earlier comment in different words now. Tetration is defined as the 1-initialized superfunction of exponentials. The previous functions discussed earilier are 3-initialized and 5-initialized, which makes them, not tetration, by definition. However, if there is an analytic continuation of the 1-initialized superfunction that overlaps with the 3-initialized superfunction, AND if on the overlap f(0) = 3, then they can be considered branches of the same function. But until that is proven, I don't think it's accurate to say that they're all "tetration". They are, however, iterated exponentials in the sense that they extend to non-integer n. And so I would probably write these functions as instead of saying that is a multivalued function that returns all three.

Messages In This Thread
RE: Should tetration be a multivalued function? - by andydude - 01/13/2016, 08:24 AM

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