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Question about speed of growth
#2
Hmm..

Ok, and if we have speed of growth of operation defined, can we say that it is a derivative of operation vs. something?

Like

d(x[4]n)/dx= w[3]n ? Or will it be d(x[4]n)/dx= (w+lnx/x )[3]n?
d(x[4]oo/dx= w[4]oo ? or d(x[4]oo/dx =(w+ln(x)/x)[3]oo ?

and my beloved:

d(h(e^(pi/2)))/d(e^pi/2) = (w+pi/2)* w[4]oo ?? ( the coefficient pi/2 may not be correct , it is just intuitive placement that if base is not e, somewhere we have to see it, the speed of growth has to be faster if x>e; it may be also (w+pi/2)[3]oo).

And again, since h(e^(pi/2))) = i

d(i)/d(e^pi/2) = (w+pi/2)[4]oo or (w+I*pi/2)[4]oo

Probably these questions have been solved in more satisfactory manner without differentiating imaginary unit and i^(1/i) in infinitary calculus mentioned by Conway in his Book of numbers , but I could not find accessible readable reference.

Excuse me for allowing myself to post such unchecked conjectures.

Ivars
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Messages In This Thread
Question about speed of growth - by Ivars - 05/16/2008, 06:05 PM
RE: Question about speed of growth - by Ivars - 05/16/2008, 10:53 PM
RE: Question about speed of growth - by bo198214 - 05/17/2008, 05:50 AM
RE: Question about speed of growth - by Ivars - 05/17/2008, 06:13 AM
RE: Question about speed of growth - by Ivars - 05/30/2008, 06:12 AM

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