03/03/2009, 10:41 PM
bo198214 Wrote:tommy1729 Wrote:since this is not really (directly) related to tetration ill post it here as ' other math '.
im intrested in Coo solutions to f(x)
given a taylor series g(x) with positive radius.
integral f(x - g(x)) dx = f(x) x.
simple ?
Is \( g(0)=0 \)?
If so you can solve it exactly by comparing the coefficients of the powerseries.
g(0) does not have to equal 0.
in fact g(0) = 1 seems more intresting.
yes , i know we can solve by comparing the coefficients of the powerseries ...
but , just as with regular iteration and similar , we can get a taylor series ...
but we wonder what ' that is '
i would like to see f(x) in terms of g(x) and elementary functions and integrals ...
" a formula " thus.
however perhaps that doesnt exist ??
regards
tommy1729