It’s purpose is obvious, but does anyone know its origin? My googlings have been in vain. I would guess that it was originally an -εν or -ιν ending that was reconstrued as ε/ι +ν and then the ν was applied to other endings, but that’s just a guess.
The origins are uncertain, but Sihler (sec. 240, pp.232-233) says it’s analogical. He suspects ἡμῖν, Lesb. ἄμμιν ~ ἄμμι as the model.