# Using a number of equations from a paper, how to mention it in my paper

I am using a number of equations from a different paper. I am using those to derive another quantity.

Is it appropriate to just mention them one after another, without stating the assumptions behind the equations etc, since I am already citing the previous paper like

Equation 1 -- (1)

Equation 2 -- (2)

Equation 3 -- (3)

.

.

.

.

.

Equation 14 -- (14)

then state the physical meaning of each parameter in the above equations?

I tried looking at some example papers but couldn't find any in the particular journal I am writing for.

If it were 1 equation, it would be fine, but I am not sure how to handle so many equations.

Or should I just reference the main equation and state the rest in the supplemental section? I just read and it seems putting too many equations in a paper is not a good idea.

• It depends on what you're writing. I normally write a brief paragraph beneath each equation which describes what the equation represents and the obvious things about it such as the parameter meanings and the reasoning for certain aspects of the equation. If I'm repeating myself in the paper I'll just refer inline to equation (1), and if I have to add MANY equations, I'll usually try to put "where the parameters \alpha, \beta, and \stuff" have their usual meanings. Unless I'm showing a set of three equations that you get at the same time from one derivation, I normally have at least some text. – la femme cosmique Aug 3 '16 at 8:22
• @lafemmecosmique That's a good approach, and the one you'd typically see in papers. However, if alpha_989 really has 14 equations, and especially if they are not self-explanatory enough, putting them in an appendix sounds more sensible to me. – 101010111100 Aug 3 '16 at 9:04
• Oh yeah, 14 equations is appendix-material for sure. Somehow I missed the '14' part ;) – la femme cosmique Aug 3 '16 at 9:05
• You want your paper to be clear and readable. Do what makes it so. – Kimball Aug 3 '16 at 9:40
• Thank you @101010111100 for your comments. I think its probably more appropriate to move it to the appendix, and cite the main equation. It was a lot of work to find the relevant equations, and connecting the dots, so I kindof thought that maybe if I put all the equations in the main body, it would kindof show the amount of work that went into finding the equations. But I guess a paper is judged not on the basis of the amount of work but on the importance of the results. Sometimes thats a hard pill to swallow. – alpha_989 Aug 6 '16 at 23:16

I'm not sure about the common practice in your field, but, as a mathematician, I feel that you have approached this thing from the wrong direction. You don't reuse equations from another paper; you reuse theorems. A theorem is a statement like

If A and B and C are true, then equations D and E hold, where the symbol F is defined as... and G is defined as...

Maybe the authors of the other paper did not formulate their result as a theorem, but it is one. It is a sloppy but common habit to throw the derivation of a result in front of the reader directly, instead of first stating it then proving it.

Another important point to note is that there are hypotheses and assumptions under which these equations hold; if you focus on equations rather than on the whole 'theorem' package, this information can very easily get lost.

So, my suggestion is: reformulate those results as theorems. It could be a single theorem with 14 separate equations as the thesis, if they are all related.

If the word theorem sounds too pompous, use proposition. If your result seems too simple to deserve this name, use lemma.

My suggestion is to use the main equation from the previous work and for the others refer the reader to the main paper.

About explaining the equation, if you give an introduction before formulating the problem, the reader would be prepared for your idea.

Moreover, you should illustrate the coherence of the equations clearly to get interests from the readers (and especially your reviewers). The recommendation is to use the graphs and plots (visual description) to notice the reader about your idea, proofs, and results.