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I am writing a research paper where I try to produce the results by using the machinery described in a different paper, i.e. testing their equations on my model.
Is it justified to use their equations by giving proper citations wherever required and submitting my paper to the journal?

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Yes, you can use equations found in other papers with proper attribution without getting into any trouble. That is how research works, you build on work of others to expand knowledge.

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    Agree, but note also that mathematics is somewhat special with regard to copyright. If there is "only one way" to express something then it isn't eligible for copyright. Equations probably fall under this exception. And, yes, cite it.
    – Buffy
    Sep 12 at 15:25
  • I might have missed something, though I believe this issue has nothing to do with copyright, but citation.
    – zabop
    Sep 13 at 5:50
  • @zabop, a citation is sufficient from the academic point of view. If the equation is reproduced from another paper, website etc., copyright is relevant, of course. But I do not believe it causes a problem in this case, I trust Buffy here (copyright is one of my smaller passions). Sep 13 at 6:09
  • @Buffy: What does copyright have to do with this? Citations are about academic integrity; copyright is a legal obligation. Since academic papers are meant to be cited, copyright law usually has various ways to ignore such citations : "only one way", but also "implied permission", "fair use" and similar ways to keep the two domains separated..
    – MSalters
    Sep 13 at 9:55
  • @MSalters, when copying you must always consider both plagiarism and copyright. I agree they are different, but either or both may apply. Copying a "significant part" of a paper may offend copyright. I just point out that math has its own concerns that might be different from other fields. Or rather, those concerns come into play more often.
    – Buffy
    Sep 13 at 10:10

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