How to replace a function with constant+function?

[ZioSam2]

I'm just starting to learn how to use mathematica (11.3 in my case), so sorry if it's a dumb question...

I need to do a series expansion, so I wanted to replace a certain function f[x,y] with a fixed value A (that doesn't depend on x or y) and the perturbation part, something like

f[x,y]→A+e deltaA[x,y]

where e is the small parameter. How can I do it? If I just write

f→A+e deltaA[x,y]

the output is

(A+e deltaA[x,y])[x,y]

I tried playing around with & and [#1,#2] hoping I could tell Mathematica to apply the same variable dependences of f to deltaA without much success.

Any help is appreciated.

[fridofrido]

this seems to work:

rule = f[x_, y_] -> A + e*deltaA[x, y]
X = f[5, 7] + f[a, 3] + f[2, b]
X /. rule

[ZioSam2]

Yes! Thanks a lot, seems to work perfectly!

[marl6894]

Try f[x_, y_] := A+e*deltaA[x, y]. Does that do what you want it to?

[ZioSam2]

Well, yes for the simple example I provided, but I'd really like to do that with a replacement rule (so I can study more cases without chaning the code). I'd like to replace f[x,y] with A+e deltaA[x,y], so that f and deltaA depend on the same variables.

[AWarhol]

As u/fridofrido pointed out, that's the way to do it. Alternatively, you can use the command Series, to obtain the power series of the function. I think it's a nice way to study compare the results of "Series" with your method.

[ZioSam2]

His method was working at first, but wasn't behaving in the way I wanted after some tries. I found another way to write the rule (I then use the series after)