As Stephen Sondheim does in HBO’s Six by Sondheim, composer Marvin Hamlisch here, in vintage film and TV clips, explains himself and his music and motivations better than anyone else. Though, in both cases, the “anyone else” group includes some of the biggest luminaries in Broadway and Hollywood. (Here, the roster includes Barbra Streisand, Woody Allen, Quincy Jones, and Christopher Walken.) Hamlisch, who died in 2012, scored hugely by composing A Chorus Line for Broadway, repopularizing the ragtime music of Scott Joplin with his movie score for The Sting, and also wrote the music for The Way We Were. But this American Masters biography by Dori Berenstein digs deeply enough to unearth some equally entertaining surprises. I had no idea, for example, that he was the young composer of an early Lesley Gore hit, “Sunshine, Lollipops and Rainbows.” Check local listings.