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 A functional equation bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 07/08/2010, 05:21 AM (07/05/2010, 07:28 PM)kobi_78 Wrote: Hi, Does anyone have an idea how to solve the following functional equation? Thanks $f(a^x) = f(x) \cdot a^x ln(a)$ 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 $\alpha$ via: $f(x)=\frac{1}{\alpha'}$ you can solve it at a fixed point via comparing the powerseries coefficients. « Next Oldest | Next Newest »

 Messages In This Thread A functional equation - by kobi_78 - 07/05/2010, 07:28 PM RE: A functional equation - by 73939 - 07/08/2010, 01:27 AM RE: A functional equation - by bo198214 - 07/08/2010, 05:21 AM

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