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Say $X=(x_1,x_2,x_3,..,x_n)$, and there is a function of $X$, which is $f(X)=g(h(c,X))$ where $c$ is constant.

Now in my case, given a $X_0$,there will be a function $i_1(x_1)$, which takes $x_1$ in $X_0$ as variable while other $x$ are fixed. I try $i_1(x_1)=g_1(h(c,x_1;X_0))$. It is kind of ugly.

So, is there any better way to write the $i_1(x_1)$? Any way people usually do? Or is this kind of notation allowed at all?

Thank you.

LSZ
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    The content of Paul's answer, inasmuch as it answers your question, is that some people write $\lambda; x. g(h(c, x; X_0))$. (You don't actually "need" much theory of lambda calculus.) Others might write $g(h(c, -; X_0))$. – user43208 Nov 10 '14 at 13:33

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You need the $\lambda$ (lambda) calculus. There are lots of textbooks and websites about it.