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+--- 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.