Abarim Publications' online Biblical Greek Dictionary
The verb πυνθανομαι (punthanomai) means to learn, but not in the sense of prolonged studying, but rather in the sense of to learn of or about a particular fact, either by serendipitous hearsay or by targeted inquiry. Depending on the context, our verb may be translated as to hear about or to ask about. A derived noun πυστις (pustis) means either inquiry or question, or news, information, report (this noun is not used in the New Testament).
Our verb πυνθανομαι (punthanomai) stems from the ancient and widely attested Proto-Indo-European root "bewd-", meaning to be awake or aware. The Sanskrit branch of this root yielded the familiar name Buddha, the Awakened One, and the title Sammasambuddho, or perfectly self-awakened one.
This PIE root survives in English as to bode (to indicate by signs) and forbode, and in Dutch as bidden (i.e. een bod doen); hence also verbieden (with "ver-", meaning anti-) and the familiar German verboten and thus forbidden. The identical Dutch verb bidden that means to pray, its German counterpart bitte and its English counterpart to bid, come from another PIE root, namely "gwedh-", meaning to ask for (a thing) rather than to ask about (information).
Our verb is used 12 times in the New Testament; see full concordance.