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The question asks for the Taylor expansion of a functional. Thus, given a real functional $f(g(x))$, what is the Taylor expansion about a function $h(x)$. What if the function is multi-variate, e.g., $f(x_1,x_2,g(x_1,x_2))$?

I've searched the web for an answer to this, and haven't come up with anything definite. If someone could help, I'd be grateful.

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    Where is your functional defined?2012-01-27
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    For simplicity consider R to R2012-01-27
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    Try to search for functional derivative. In essence, you have to write $f(h(x) + \epsilon \delta g(x))$ and then perform a normal Taylor expansion in $\epsilon$ setting $\epsilon=1$ at the end (but keeping $\delta g(x)$ small.2012-01-27
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    I was hoping for a little more elaboration.2012-01-28

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