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 A functional equation kobi_78 Junior Fellow Posts: 11 Threads: 3 Joined: Dec 2009 07/05/2010, 07:28 PM (This post was last modified: 07/05/2010, 07:29 PM by kobi_78.) Hi, Does anyone have an idea how to solve the following functional equation? Thanks $f(a^x) = f(x) \cdot a^x ln(a)$ 73939 Junior Fellow Posts: 12 Threads: 3 Joined: Jun 2010 07/08/2010, 01:27 AM $f(x)=f(x^1)=f(1)x\ln(x)$ Let's start there. Then, we plug in 1 to get $f(1)=0$. Then $f(x)=0$. bo198214 Administrator Posts: 1,395 Threads: 91 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 »

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