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A functional equation
#1
Hi,

Does anyone have an idea how to solve the following functional equation?

Thanks

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#2

Let's start there. Then, we plug in 1 to get . Then .
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#3
(07/05/2010, 07:28 PM)kobi_78 Wrote: Hi,

Does anyone have an idea how to solve the following functional equation?

Thanks


Thats called "Julia equation", generally
f(F(x))=F'(x)f(x) to solve for f.

You obtain an Abel function from it, or obtain it from an Abel function via:


you can solve it at a fixed point via comparing the powerseries coefficients.
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