For all his international success, Billy Joel still tends to be identified as a Long Island singer-songwriter, in much the same way Bruce Springsteen is identified with the Garden State. Joel even began his career with an album entitled Cold Spring Harbor, after a peaceful hamlet on L.I.'s north shore, near his widely reported birthplace, Hicksville. Yet in Billy Joel Live at Yankee Stadium, put together from two sold-out 1990 performances at The House That Ruth Built, the multi-platinum superstar says the concerts represented a homecoming to his birthplace, the Bronx. We'll take Joel at his word on the Bronx-born claim. (Since his considerable gifts for songsmithing clearly draw on the rich doo-wop traditions of the Bronx in the 1950s, one could argue that his music was born there.) So it's easy to get into the spirit of the production, which starts with Joel arriving along with his fans on the subway and entering the stadium gates alongside the appreciative hordes. Once on stage with his band and touring accompanists, though, he's The Entertainer, swinging for the fences with spectacular lights and thundering orchestration. Opening with "Storm Front," Joel barrels through high-energy hit after hit, pounding the keys through such favorites as "I Go to Extremes" and "Scenes from an Italian Restaurant" before switching from piano to tempered accordion on "Downeaster 'Alexa.' " He straps on a guitar for "We Didn't Start the Fire," covers the Isley Brothers' classic "Shout," and delivers the anthem "A Matter of Trust" with appropriate vigor. The 13-song set closes with "Piano Man," a cozy classic closely identified with his Long Island lounge roots, and somehow before 40,000 or so fans in baseball's most storied stadium, Joel manages homey intimacy. You'd think he was born there.