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Principal Branch of the Super-logarithm
#8
(11/17/2007, 10:58 AM)andydude Wrote:

i do not think that is correct ...

it is tempting to substitute x => x + pi and similar tricks but in general



is false. take for example x-> x^3



is false because slog is not a "modified" inverse super of !

so i think this is a mistake ... i would prefer a better explaination then my own very much Dodgy

perhaps this is the reason that we do not have many ( or many known ? ) calculus identities related to tetration ; substitution is troublesome , hence together with the growth speeds , integrals are harder or even impossible to express in closed form.

i feel im missing something here and im still a bit confused about this...

( although i can unfortunately not ask for a concrete question - apart from the one below - , just an elaboration )

i must say i wonder about the existance of the following

h and g do not commute :



derivate



substitute



integrate



( * notice how h'(x) is on both sides as if it does not matter if we differentiate with respect to it , or just substitute directly , which mainly motives this question btw )

???
***

it appears that " -1 " is a function of f and g in any , or at least my imagination tells me.

so maybe we should define , or could define for some functions :



or



or something similar ??

so another question becomes





regards

tommy1729
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Messages In This Thread
RE: Principal Branch of the Super-logarithm - by tommy1729 - 06/20/2011, 09:32 PM

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