The effect of Luke"s omission of the conversation Jesus had with the disciples about Elijah is clear. This healing appears as the work of the Son of God whom the Transfiguration presented. [source][source][source]
"It is the Jesus who has been transfigured who now appears to help men at the foot of the mountain; what the disciples cannot do, he can do. He appears like a visitor from another world who has to put up with the unbelief of men." [1][source]
Luke also omitted Jesus" teaching on the importance of faith that He gave His disciples at the end of this story (cf. Matthew 17:19-20; Mark 9:28-29). All Luke"s emphasis falls on Jesus" authority. This is the first of four incidents that show the disciples" lack of faith, slowness to learn, pride, and intolerance. [source][source][source]