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+--- Thread: other math ... equation (/showthread.php?tid=247)
other math ... equation - tommy1729 - 03/03/2009
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 ?
RE: other math ... equation - bo198214 - 03/03/2009
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.
RE: other math ... equation - tommy1729 - 03/03/2009
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
RE: other math ... equation - bo198214 - 03/03/2009
tommy1729 Wrote: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 ??
Mostly those formulae dont exist (outside school mathematics
).
RE: other math ... equation - tommy1729 - 03/03/2009
bo198214 Wrote:tommy1729 Wrote: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 ??
Mostly those formulae dont exist (outside school mathematics
what do you mean by " outside of school math " ?
i dont get the message nor the humor ?
are you trying to say , apart from some trivial cases thought in school ?
like perhaps g(x) = sqrt(x+1)
regards
tommy1729