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 weird series expansion tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 07/05/2010, 04:32 PM (This post was last modified: 07/05/2010, 07:58 PM by tommy1729.) consider F(x) a real-analytic function mapping R+ to R+ with only a single fixpoint, the one at 0. let g(x,n) be g(g(x,n-1),1) and g(x,1) = arcsinh(x/2) F(x) is strictly nondecreasing. F(x) grows slower than x^2 + 1. let a_n be real. the following weird series expansion has come to my mind : a0 + a1 x + a2 g(x,1) + a3 g(x,2) + a4 g(x,3) + ... and many questions pop up. regards tommy1729 73939 Junior Fellow Posts: 12 Threads: 3 Joined: Jun 2010 07/05/2010, 07:27 PM g(x,n) = g(g(x,n-1)) The right side of the equation uses g as a function on one variable. How is g(x) defined? tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 07/05/2010, 07:59 PM i corrected it ... should be clear now. « Next Oldest | Next Newest »

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