What is the ruling on raising the hands when saying "Allahu Akbar" for the prostration of recitation (sujood al-tilawah), whether inside or outside of prayer?

The prostrator does not raise his hands when going down for the prostration of recitation (Sujud al-Tilawah), according to the consensus of the four madhhabs, whether in prayer or outside of it.

The majority (Hanafis, Malikis, Hanbalis, and some Shafi'is) hold that there is no opening takbir (Takbirat al-Ihram) for theudu of recitation. Rather, one says the takbir when going down without raising the hands, basing their argument on what Abu Dawud narrated from Ibn Umar, that the Prophet, peace and blessings be upon him, would say the takbir and prostrate when passing by a verse of prostration.

While most Shafi'is hold that outside of prayer, one says the opening takbir with raised hands, then says a second takbir when going down without raising the hands.

Ibn Taymiyyah is of the view that there is no salam for the prostration of recitation, and that it is an innovation, and no opening takbir. Rather, takbir was only reported for rising or descending.

In summary, hands are not raised when going down for prostration, by consensus. The preferred opinion is that of the majority, which states that raising the hands is not legislated, neither for the opening takbir nor for going down.