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Trivia
I am using Taylor series expansions to solve a system of PDEs for a number of functions $f_1(z, \phi), f_2(z, \phi) ...$ The expansions are generated by Series command.

The functions are expanded in $z$ around $z=0$, and therefore, the coefficients of the series are functions wrt $\phi$, e.g. $f_1^{(0,1)}[0,\phi]$, $f_1^{(1,2)}[0,\phi]$. Here $f_1^{(a,b)}[0,\phi]$ reads as a-th order coefficient in the expansions of $f_1[z,\phi]$, differentiated $b$ times wrt $\phi$.


Question
Suppose that I have found $f_1^{(a,0)}[0,\phi] = g[\phi]$.
I want to be able to substitute it as a function, i.e. something like f1[0] -> Function[x, g[x] ], to evaluate expressions like
$f_1^{(a,2)}[0,\phi]+(f_1^{(a,1)}[0,\phi])^2\qquad$ to $\qquad g''[\phi] + (g'[\phi])^2$

How should I implement it?

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Ok. Sorry, it was a trivial question

If we know that e.g. $f_1^{(1,1)}[0,\phi] = g[\phi]$ then

Derivative[1,n_Integer][f1][0, phi] :> D[g[phi], {phi,n}]
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