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 2*sinh(3^h*asinh(x/2)) is the superfunction of (...) ? Gottfried Ultimate Fellow Posts: 757 Threads: 116 Joined: Aug 2007 09/10/2013, 12:23 PM (This post was last modified: 09/10/2013, 12:31 PM by Gottfried.) I was studying the function $f_a(x) = 2 \cdot \sinh ( a \cdot \sinh^{-1}(x/2))$ finding that for odd a this gives (finite) polynomials in x with integer coeffcients - thus for integer x and odd a this is integer and for rational x this is also rational. (For even a replace sinh by cosh). So this is somehow interesting. Formally this looks like the Schroeder-function of some unknown function $f_a(x)$ (with some parameter a), where also the iteration-height h is introduced: $f_a^{[h]}(x) = 2 \cdot \sinh( a^h \cdot \sinh^{-1}(x/2))$ Is this function $f_a(x)$ something common in our usual, daily toolbox? Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread 2*sinh(3^h*asinh(x/2)) is the superfunction of (...) ? - by Gottfried - 09/10/2013, 12:23 PM RE: 2*sinh(3^h*asinh(x/2)) is the superfunction of (...) ? - by tommy1729 - 09/10/2013, 09:50 PM RE: 2*sinh(3^h*asinh(x/2)) is the superfunction of (...) ? - by tommy1729 - 09/10/2013, 10:06 PM RE: 2*sinh(3^h*asinh(x/2)) is the superfunction of (...) ? - by mike3 - 09/11/2013, 10:49 AM RE: 2*sinh(3^h*asinh(x/2)) is the superfunction of (...) ? - by Gottfried - 09/11/2013, 06:30 PM RE: 2*sinh(3^h*asinh(x/2)) is the superfunction of (...) ? - by Gottfried - 09/11/2013, 08:32 PM

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