 weird series expansion - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: weird series expansion (/showthread.php?tid=469) weird series expansion - tommy1729 - 07/05/2010 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 RE: weird series expansion - 73939 - 07/05/2010 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? RE: weird series expansion - tommy1729 - 07/05/2010 i corrected it ... should be clear now.