I want to cite an equation in my thesis that has a minor typo in the cited source (the wrong letter is used for an index). How should I do that? Can I simply correct the typo in my paper without commenting on it, or should I indicate somehow that the equation has been altered? I’m supposed to use APA style.
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You should indicate what the typo was and that you corrected it. This will prevent your readers getting confused if/when they look up the reference, and related annoyances (e.g., the referee accusing you of making an error, your professor giving you a bad grade, or people generally just thinking you are sloppy). Noting the correction will also create a historical record of the typo, which could be useful for other researchers working on the same topic in the future.
Related discussion for a non-mathematical correction: Quoting a typo: Do I really have to do "sic", or can I just fix the sentence?

Dan Romik
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13Could be a case where a footnote does the job. Cite as usual and explain the correction in the footnote. – Snijderfrey Mar 10 '21 at 19:52
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4@Snijderfrey, footnotes are fine in general, but not permitted with every "style". – Buffy Mar 10 '21 at 19:56
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8Sure, a footnote is an appropriate way to mention it. I think I did exactly that in a recent paper of mine. – Dan Romik Mar 10 '21 at 19:56
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How do you use foot notes in an equation? A ¹ or ² can easily be confused with an exponent. – Michael Mar 11 '21 at 11:19
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4@Michael I assume that there will be some text introducing the equation, and you can place the footnote there. – Snijderfrey Mar 11 '21 at 13:07
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@Michael as Snijderfrey says, the footnote is attached to the surrounding text rather than placing the marker in the equation itself. – Dan Romik Mar 11 '21 at 13:59
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3@Michael There's an xkcd for that. – Angew is no longer proud of SO Mar 11 '21 at 15:06
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@Michael symbol footnotes *, †, etc., or alphabetical would help, though clearly not in all cases. Quite a lot of Physics journals use numeric superscript citations and with a little care that's not a problem – Chris H Mar 11 '21 at 15:59