Remark on Gottfried's "problem with an infinite product" power tower variation

[tommy1729]

Remark on Gottfried's "problem with an infinite product".


http://math.eretrandre.org/tetrationforu...hp?tid=785

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A similar case occurs with power towers.

g(x) = x ^ f(x) ^ f^[2](x) ^ ...

An intresting case is ln(x) ^ ln(ln(x)) ^ ln^[3](x) ^ ... = A(x).

Let x >> 10.

Define f(x) = arcsinh(x/2)
( YES I USE THIS AGAIN , THE INVERSE OF 2SINH !!! )

Now there exists (small) constants C1,C2,C3,C4 such that

f(x) ^ f^[2](x) ^ f^[3](x) ^ ... ~ C1 (x + C2)^C3 + C4

Nice.



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tommy1729