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 2*sinh(3^h*asinh(x/2)) is the superfunction of (...) ? tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 09/10/2013, 09:50 PM (This post was last modified: 09/10/2013, 09:56 PM by tommy1729.) Hi Gottfried Once again we see this 2sinh function !! Im thinking about this function too, together with my friend mick. I assume you know very well that when given $f(x)$ we can compute that it is the superfunction of $g(x)$ where $g(x)=f(f^{-1}(x)+1)$. Although that formula does not simplify the expression if that is even possible. There are many named (odd) polynomials in math and I am reminded that the similar looking (problem) $sin (n arcsin(x))$ and related ones are connected to ChebyshevPolynomials (of the First or Second Kind for example) and other named polynomials that are usually defined by differential equations. So I guess we could say it is an iteration of the g-formula above for some named polynomials. But I doubt that answers your questions. Notice that - just like the Riemann hypothesis - the zero's of $2sinh((2n+1)arcsinh(z/2)) = 0$ All lie on a critical line !! Hint: $cos(pi*m/(4n+2)) i$ !! Im not sure how to answer your question more. I guess we need to look at some named polynomials and their recursions. Further just like the addition formula for sine was usefull , the same is probably true for this $2sinh$ !! Btw did you read my fermat superfunction post ? Elementary functions are still underrated ! regards tommy1729 « 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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