With Nelson Riddle conducting the band, Frank performs the Rodgers and Hart song "The Most Beautiful Girl in the World" (from the 1935 musical Jumbo; hello, Prince!). This fast tempo version of the song is the Riddle arrangement used for Sinatra's 1966 Strangers in the Night LP. The performance is from the television special of the same year, Frank Sinatra - A Man and His Music Part II.
Some typical, cornball, Hoboken-born-and-bred humor at the end:
I haven't sung that fast since they raided the band bus, and threw Joe Bushkin in the clink...
Sinatra was jealous of Dean Martin's seemingly effortless ability to tell jokes and get laughs from an audience. You can see why. Dean's secret? He just didn't care.