Francis Albert Sinatra celebrated his 75th birthday Wednesday by doing what he does best - singing on stage, alone in the spotlight.

The sold-out Diamond Jubilee Concert at the Meadowlands' Byrne Arena, East Rutherford, N.J., was only a few miles from Hoboken, where Ol' Blue Eyes was born Dec. 12, 1915.Sinatra, accustomed to doing it his way, planned the performance down to the minutest detail and rehearsed it with a warm-up concert at the arena Tuesday.

Some 20,800 fans paid from $35 to $50 each for Wednesday concert seats to hear the popular American singer give his familiar renditions of "My Way," "New York New York," "Strangers in the Night," "Summer Wind," "Mack the Knife" and many others favorites.

The nation will share in Sinatra's birthday party Sunday when CBS-TV will air a two-hour musical salute to him and his career featuring Harry Connick Jr., the 23-year-old New Orleans singer who is mentioned as Sinatra's successor, Gene Kelly, Tony Bennett, Ella Fitzgerald and Paul Newman.

Columbia, Capitol and Reprise Records are marking the yearlong celebration with selective compilations of his work, which encompasses an era that began with 78s and continues the beat with CDs. Included are 228 of Sinatra's 1,700 recordings, which would take four days to play in their entirety.

For those who want to wish Sinatra a happy birthday personally, there is a Sinatra Hotline, 1-900-420-CHIVAS, to receive greetings throughout the Diamond Jubilee Year at $2 a call, the money going to charity. Jill St. John, a leading lady in several Sinatra movies, was the first well-wisher.

Sinatra will be celebrating throughout 1991 with one of his most ambitious world tours, including Europe, South America, Japan and Australia and several cities in America.