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Elmore Leonard -- the legendary writer behind "Get Shorty," "3:10 to Yuma" and "Justified" -- has died, three weeks after suffering a stroke ... TMZ has learned.

We're told Leonard passed away at his home in Detroit ... the city where he lived since 1934.

E.L. is a legend -- dozens of his novels and short stories have been transformed into movies or TV shows ... including "Out of Sight," "Be Cool," "Hombre," "Mr. Majestyk" and "3:10 to Yuma."