Alrahman and Alraheem (the root)

[nimnimak_11]

Peace

I've been trying to better understand the meanings of alrahman and alraheem. So i cheked the root of the word on PRL and Lane Lexicon and found something which I don't understand:

Rahman - it is active participle noun in the measure of fa'lan which conveys the idea of fullness and extensiveness.
Rahim - it is in the measure of fa'il which denotes the idea of constant repetition and giving

What is fa'lan and fa'il? Is the root of these two words: ف ع ل
Fa-Ayn-Lam?

Any help would be much appreciated