Perhaps the greatest at piano improvisation, I think I hear at least one piece by John Coltrane each day on the radio.
Thelonious Monk, equally adept at the piano and at sporting a jaunty pinstripe.
Another tragic musician [there really is no shortage in that category], Chet Baker set his own style with both the trumpet and, apparently, the suede Trilby.
Ironically not as well known as the others, Sonny Stitt toured more and was recorded more than almost any other jazz musician during the great age. So as not to be confused with Charlie Parker, who played the alto sax, Stitt became a virtuoso of the tenor sax. Even in casual moments such as that pictured, you get a sense of what was a remarkably graceful stage presence.