In a way that is powerfully persuasive or forces attention; in a manner that strongly drives or urges someone forward.
From compelling (present participle of compel, meaning 'strongly persuasive') plus the adverbial suffix -ly. The root is Latin compellere (to drive together).
Compellingly is one of the few words from the compel family that thrives in modern English, especially in book reviews and criticism. People say a story is 'compellingly written' because it means the prose doesn't just persuade—it practically drags you through the narrative.
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