What is the expiation for someone who has repeatedly sworn falsely out of ignorance, and is he required to fast all those days?

A false oath is considered a "Ghamus Oath" (a sinful, immersive oath) and is one of the major sins. Repentance (Tawbah (definition) Nasuh) to Allah is obligatory, and according to the majority of scholars, there is no expiation (kaffarah (definition)) for it. However, the Shafi'is hold that expiation is obligatory along with repentance. If the false oath was taken out of necessity due to fear of severe harm, there is no sin, but using subtle phrasing (tawriyah) is preferable. Frequent swearing is blameworthy in Islamic law, as Allah Almighty says: "And do not obey every [worthless] habitual swearer" (Al-Qalam: 10), and His saying: "And guard your oaths" (Al-Ma'idah: 89). If the oath was a casual, unintentional utterance (laghw), then the rulings of an oath do not apply to it. As for a truthful oath that was broken, expiation is required by feeding or clothing ten needy persons, or freeing a slave; if one is unable, then fasting for three days. If you are unsure about the number of expiations, take the minimum certain number, but it is more cautious to make expiation for all that you are unsure about. Ignorance of the expiation or punishment that results from an oath is not an excuse. Sincere repentance and abundant good deeds are recommended.