profound knowledge; extensive learning
A formal, somewhat literary set phrase describing deep, wide-ranging knowledge. Often used in academic or intellectual contexts.
He possesses profound knowledge.
I am always amazed by that professor's extensive learning.
博識 is a more common, neutral noun meaning 'wide knowledge' or 'erudition'. 該博な知識 is a more formal, emphatic phrase emphasizing both depth and breadth.
該博 (がいはく) means 'extensive, profound' and is a somewhat formal term. Combined with 知識 (ちしき, 'knowledge'), it forms a set phrase. The exact historical derivation of 該博 is uncertain, but it is conventionally associated with deep, wide-ranging learning.