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I want to define a function that contains other functions but with other variables. Is it possible?

For example, I would like to do something like this:

A[x_, y_] = 2 x + y;

Now, some calculations on A, derivatives, and later:

B[a_, b_] = A[x,y]/.{x -> a Cos[b], y -> a Sin[b]}.
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    $\begingroup$ Use := instead of = while defining the functions. $\endgroup$
    – Syed
    Mar 1 at 14:00
  • $\begingroup$ Thanks, in this case, it works. But, generally, is this possible, when I cannot use := at the beginning? Generally, I am working with Eigensystems, so my first assignment, as I read, must be: A[x_,y_] = Eigenvalues[...][[1]]; $\endgroup$
    – blahblah
    Mar 1 at 14:05
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    $\begingroup$ You may directly define: B[a_, b_] = A[ a Cos[b], a Sin[b]] $\endgroup$ Mar 1 at 14:09
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    $\begingroup$ Please improve the question by including a minimal example so that you receive an applicable answer. $\endgroup$
    – Syed
    Mar 1 at 14:20
  • $\begingroup$ Along the lines of @DanielHuber, B[f_][a_,b]:= f[a_,b_] (e.g., B[ArcTan][1,1] $\endgroup$ Mar 1 at 17:11

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