Jamieson, Fausset and Brown on 2 Kings 2:9

9. Elijah said unto Elisha, Ask what I shall do for thee--trusting either that it would be in his power to bequeath it, or that God, at his entreaty, would grant it.

let a double portion of thy spirit be upon me--This request was not, as is commonly supposed, for the power of working miracles exceeding the magnitude and number of his master's, nor does it mean a higher endowment of the prophetic spirit; for Elisha was neither superior to, nor perhaps equally great with, his predecessor. But the phrase, "a double portion," was applied to the first-born [De 21:17], and therefore Elisha's request was, simply, to be heir to the prophetic office and gifts of his master.