04/25/2010, 02:34 PM
(04/25/2010, 10:53 AM)bo198214 Wrote: Is there an elementary real function \( F \), such that
\( F(1+F^{-1}(x)) \) is a real polynomial of degree at least 2 without real fixed points.
this question or similar has occured before.
some papers have been written about it , i considered similar questions and i believe it appeared on the math forum ...
ill have to dig ...
i believe hypergeometric solutions were found ...
but sometimes a hypergeo can be expressed by elementary functions ...
personally i considered inverse hypergeometric functions , but those also can be simplified sometimes.
so im optimistic ...
have you tried simple cases such as a*exp(b^x)*exp(c*x) + d ?