Both الرَّحْمَٰنِ and الرَّحِيمِ begin with the article before rāʾ, a sun letter. Therefore the article lām assimilates into rāʾ, shown by the shaddah.
The rāʾ has fatḥah and is pronounced heavily. These are two separate decisions: assimilation due to rāʾ following the article, and heaviness due to the rāʾ's vowel. Do not insert an audible separate lām.
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The sun-letter lām in ar-Raḥmān and ar-Raḥīm
Al-Fātiḥah: Integrated Tajwīd, Madd and Pausing Practice
Both الرَّحْمَٰنِ and الرَّحِيمِ begin with the article before rāʾ, a sun letter. Therefore the article lām assimilates into rāʾ, shown by the shaddah.
The rāʾ has fatḥah and is pronounced heavily. These are two separate decisions: assimilation due to rāʾ following the article, and heaviness due to the rāʾ's vowel. Do not insert an audible separate lām.