What is the ruling on a doctor who made a mistake by administering an overdose to a two-month-old sick child during treatment, which caused its death, and how does he expiate for that?

If a specialist doctor makes a mistake and gives a patient an overdose that leads to their death, he is obligated to offer expiation for accidental killing by freeing a believing slave. If he cannot find one, then by fasting for two consecutive months. The blood money (diyah) is to be paid by his 'aqilah (male relatives on the father's side) or from the public treasury (Bayt al-Mal), and it can be waived by the heirs. However, the expiation is not waived. There is no sin upon him as long as he is a specialist and intended nothing but treatment.