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.
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?