Born in 1916 in Copenhagen to German parents, he started working professionally at the age of 17 and enjoyed a career which spanned eight decades.
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He accompanied many of the greats of 20th century popular music, including Fats Waller, Edith Piaf, Django Reinhardt and Lionel Hampton.
"I am often accused of being a chameleon," Asmussen, who also acted and painted, told a Danish newspaper last year.
"I must say that I broadly agree. I am always embarking on different projects."
Asmussen died just weeks short of his 101st birthday on February 28.
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