Luke Goose, also known as Luke the Goose, is an anthropomorphic goose.
This spectacles-wearing goose is a well-respected member of Duckburgian society. Luke Goose works as a genealogist, and he is said to have drawn an in-universe equivalent of Don Rosa's Duck Family Tree.  By most accounts, Luke is the husband of Fanny Coot and the father of Gus Goose, although there exist alternative accounts which instead claim that he was the husband of Daphne Duck and birth father of Gladstone Gander, with Gus instead being his nephew.
Behind the scenes
Luke Goose first appeared in Carl Barks's story Jet Witch, although his name and role as Gus Goose's father were created for Barks' 1950's version of the Duck Family Tree; there, he was actually Gus Goose's uncle and Gladstone Gander's real father, with Goosetave Gander being merely Gladstone's adoptive father. Carl Barks would, however, later alter this for his second Duck Family Tree, which is the basis of Don Rosa's version and is now considered the canonical version by the broadest audience.