What is the expiation for one who swore by Allah concerning a matter he believed to be true, but then it became clear to him that it was false?

Intentionally making a false oath is one of the major sins and is called "Al-Yameen Al-Ghamoos" (the dip-in-sin oath), as the Prophet, peace and blessings be upon him, said: "The major sins are: associating partners with Allah, disobedience to parents, killing a soul, and Al-Yameen Al-Ghamoos." As for swearing based on a presumption, or what slips from the tongue unintentionally, that is considered "laghw al-yameen" (idle oath) for which Allah does not hold one accountable, as Allah Almighty says: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what your hearts have earned." There is no expiation for one who swears unintentionally. It is disliked to swear excessively without need.