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2*sinh(3^h*asinh(x/2)) is the superfunction of (...) ?
#6
ahh, stupid....

Of course the basic Chebychev-polynomials are "the-functions-of which-acosh(x)-is-the-Schröderfunction".

Let for instance then of course the iterates and the iterates to any height h are which can then be evaluated/interpolated using the cosh/acosh-pair as .

So my question is then -very simple- answered for "base=2" that the "more common" function "in our toolbox" is the quadratic polynomial (where the fractional iterates become power series instead...).

And if I take any higher-indexed Chebychev-polynomial as the base-function , the iterate is simply computable by the cosh/acosh-mechanism

(And for my initial question using sinh/asinh it is simply the same except with other polynomials)


Should have seen this before... -

Gottfried

[update]: And -oh wonder- this is just related to a question in MSE where I was involved this days without knowing that this two questions are in the same area; I just added the information about the cosh/arccosh-composition there... :-) http://math.stackexchange.com/questions/...965#490965
Gottfried Helms, Kassel
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RE: 2*sinh(3^h*asinh(x/2)) is the superfunction of (...) ? - by Gottfried - 09/11/2013, 08:32 PM

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