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Functional super-iteration and hierarchy of functional hyper-iterations
#2
Yes, some years ago I thought about a similar hierarchy, though in a different context of converting exponential binary trees into analytic functions.

To give an impression of this operator I compute the first three functions starting with . To make the notation more extensible I use for the operator, that maps to .

,
,
,

And of course next we would put into the exponent of the operator and so on, getting nice hierarchy of just too quickly growing functions.

This hierarchy can already be built on positive integer functions, so no analytic something needed.
I guess the growth of is equal to the growth of .
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RE: Functional super-iteration and hierarchy of functional composition-based operations - by bo198214 - 05/02/2009, 07:48 AM

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