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nested logs ?
#1
similar to continued fractions and nested radicals , i was thinking once again about " nested logs "

a0 + b0 ln( a1 + b1 ln( a2 + b2 ln( ...

which seems like the natural tetrational analogue to continued fractions and nested radicals.

however i was unable to produce anything nontrivial of value or beauty with this idea ...

maybe we can express functions with this ?

ofcourse both a_n and b_n being both constant is not intresting...
how about a_n = 2^^n , b_n = constant ?

i would not be amazed if i was not the first person with this idea , so is there hope ??

tommy1729
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#2
Quote:The penchant for formulas and bounds containing a profusion of nested logarithms has led to the following joke. What sound does a drowning analytic number theorist make? A: log log log log... (Havil 2003, p. 115).

http://mathworld.wolfram.com/NestedLogarithm.html
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#3
i was already aware of both the joke and that page.

however that page is quite empty if one ignores the fancy pics and it does not seem helpfull ... ( maybe the ref ?? )
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