08/31/2007, 10:21 PM
Well, unfortunately, no magic at all. Formulas 1 and 2 can be easily obtained, taking into account the hyperoperational properties of tetration, e.g..:
e#(x-1) = ln(e#x)
as well as the definition of the product logarithm:
if x . e^x = z then: x = ProductLog[z].
However, it is interesting to remind that the product logarithm is a complex function, with two real branches. I shall come back to it.
Please see the attached short pdf comment. I am too lazy to insert it in this text.
GFR
e#(x-1) = ln(e#x)
as well as the definition of the product logarithm:
if x . e^x = z then: x = ProductLog[z].
However, it is interesting to remind that the product logarithm is a complex function, with two real branches. I shall come back to it.
Please see the attached short pdf comment. I am too lazy to insert it in this text.
GFR
