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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 ?

Posts: 1,386

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Joined: Aug 2007

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

?

If so you can solve it exactly by comparing the coefficients of the powerseries.

Posts: 1,358

Threads: 330

Joined: Feb 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 ?

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

Posts: 1,386

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Joined: Aug 2007

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

).

Posts: 1,358

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Joined: Feb 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