My children ask me to recite surahs from the Quran whilst they are falling asleep in bed next to me, is it ok to recite to them whilst laying in bed without head covering? Or should I sit up and wear head covering before reciting? And must I have wudhu to recite even if its reading from memory and not touching any text?

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Head covering for Quran recitation is not obligatory. If it’s memorisation and not touching the words then wudhu is not necessary