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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?

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    Could be a case where a footnote does the job. Cite as usual and explain the correction in the footnote. – Snijderfrey Mar 10 at 19:52
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    @Snijderfrey, footnotes are fine in general, but not permitted with every "style". – Buffy Mar 10 at 19:56
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    Sure, 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 at 19:56
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    @Michael I assume that there will be some text introducing the equation, and you can place the footnote there. – Snijderfrey Mar 11 at 13:07
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    @Michael There's an xkcd for that. – Angew is no longer proud of SO Mar 11 at 15:06

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