The general rule is that hamzat al-waṣl drops when its word is joined to preceding speech, but it is pronounced at the beginning. The source then explains how to determine its starting vowel.
Compare starting directly at ٱسْمُ رَبِّكَ with entering the same word from a previous word. A fresh start needs the facilitating vowel; a connected reading normally does not.
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Dropping waṣl in connected reading
Rules of Hamzah — Taḥqīq, Tashīl, Ibdāl and Hamzat al-Waṣl
The general rule is that hamzat al-waṣl drops when its word is joined to preceding speech, but it is pronounced at the beginning. The source then explains how to determine its starting vowel.
Compare starting directly at ٱسْمُ رَبِّكَ with entering the same word from a previous word. A fresh start needs the facilitating vowel; a connected reading normally does not.