The equation $f(f(x))=xe^x=x+x^2+\frac{x^3}{2}+\frac{x^4}{t}+\dots$ f(f(x))=xe^x=x+x^2+\frac{x^3}{2}+\frac{x^4}{6}+\dots$ has a unique formal powerseries solution. Is its convergence radius 0 as was shown by Baker for the equation $f(f(x))=e^x-1$? Or more generally: Let $F(x)=xe^x$ does the unique formal powerseries solution of $F(f_t(x))=f_t(F(x))$ with $f_t(x)=x+t x^2 +\dots$ have convergence radius 0 for all non-integer numbers $t$?
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fractional iteration of $xe^x$ has zero convergence radius?The equation $f(f(x))=xe^x=x+x^2+\frac{x^3}{2}+\frac{x^4}{t}+\dots$ has a unique formal powerseries solution. Is its convergence radius 0 as was shown by Baker for the equation $f(f(x))=e^x-1$? Or more generally: Let $F(x)=xe^x$ does the unique formal powerseries solution of $F(f_t(x))=f_t(F(x))$ with $f_t(x)=x+t x^2 +\dots$ have convergence radius 0 for all non-integer numbers $t$?
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