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The senses whose referents include Southeast Asia are from East Ind(ies) + -ian. The sense specific to eastern India is from East Ind(ia) + -ian.
Etymology from Wiktionary, CC BY-SA 4.0.
East Indian
Today it means: Of or pertaining to the people, products, or culture of Southeast Asia, particularly the Malay Archipelago, Sri Lanka, or India. Full definition →