how to cite an equation that is common knowledge but I use others notation

Question

I am writing my masters thesis on an econometrics topic. It is very closely related to another paper by NW. Since our papers are very closely related, I am using their notation in order to draw comparisons (which I state before introducing my model).

NW motivate their model using known findings from their field. They demonstrate that the standard model does not behave well under their assumptions by (mathematically) decomposing the standard model's objective function. This approach is very common, however, every author formats their arguments to fit their purpose. In my paper, I want to build on NWs argument. I.e. I want to make the same point and extend it. Do I need to cite their equation (the decomposition of the objective function) in any special way?

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To paraphrase what I currently have:

... NW illustrate this by deconstructing the expectation of the objective function into a signal term and a noise term

$$E[Q(\beta)] = Eg(\beta)'Wg(\beta) + tr(W Omega(\beta))$$

...

(I copy their notation exactly.)

The reason I am unsure is that NWs argumentation is not unique to their paper but how they frame it is.

Answer 1

You seem to have a very mechanistic view of citation, as if there were a set of rules that tell you how to write a citation in every possible (or, at least, common) situation. That's not how it works. Think about what the purposes of citation are, and cite material in a way that is appropriate to those purposes.

Here, there are two intellectual contributions you might wish to cite: the underlying equation and the notation you've used to express it. If the equation is common knowledge, do you need a citation for it at all? Or would a "see, e.g., [textbook]" or "as introduced by [original source]" citation be more appropriate? Given that you're using the notation throughout your paper, isn't it enough to say once that you use the notation of NW? That gives appropriate credit and informs the reader where they can find more information.

Answer 2

You can use your paraphrase as-is. In addition, since NWs argumentation is not unique, you might like to add further context and mention other works. E.g., precede your paraphrase with an introduction to the wider literature in the area.