In yoel 2:27 The pasuk states
וִידַעְתֶּ֗ם כִּ֣י בְקֶ֤רֶב יִשְׂרָאֵל֙ אָ֔נִי וַאֲנִ֛י
What is the difference in nekudot usage of the words אני? More specifically, the difference between chataf patach alef (אֲ) and kamatz alef (אָ)?
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There is no difference in meaning between אֲנִי and אָנִי. Rather, the difference is contextual: the latter is the so-called pausal form of אֲנִי. Pausal forms appear (usually) on strong pausal te'amim, and correspond to rhetorical pauses/emphases (that is, pauses/emphases in recitation of the text) and often have longer vowels (corresponding to slower reading).
Some other examples are: גֶּפֶן to גָּפֶן (from the bracha on wine, but also Gen 40:9 vs Hos 14:8); חָפְרוּ to חָפָרוּ (Gen 21:30 vs Gen 26:32); אֵלְכָה to אֵלֵכָה (Gen 24:56 vs Gen 30:26). An interesting verse is Deut 13:5, all of whose verbs are in pausal form, presumably for rhetorical purposes.
English has something similar. Wikipedia has the example of the vowel in "can" in "I can do it" vs "I can do it".