By Dave Warner

LOWER MERION, Pennsylvania (Reuters) - More than 1,000 people bid farewell on Tuesday to former U.S. Senator Arlen Specter at a service featuring tributes by family and dignitaries and concluding with Frank Sinatra's "My Way."

Specter died at his Philadelphia home on Sunday after battling non-Hodgkin's lymphoma. He was 82.

U.S. Vice President Joe Biden and former Pennsylvania Governor Ed Rendell were among the mourners.

In Washington, U.S. President Barack Obama ordered flags to be flown at half-staff at federal installations and facilities across the nation.

"Arlen Specter was an elected official in Pennsylvania for 38 years and I can say without any fear of contradiction, he had more of a positive effect on the lives of Pennsylvanians than anyone in the history of the commonwealth, with the possible exception of Ben Franklin," Rendell said. "I don't say that lightly."

Specter served two terms as Philadelphia district attorney, from 1966 to 1974, and 30 years as a U.S. senator.

He played a pivotal role in many major issues of his time, including the investigation into the assassination of President John Kennedy, disputes over controversial Supreme Court nominees and the Senate vote not to remove President Bill Clinton from office for perjury after an affair.

An independent-minded moderate, Specter was spurned by Pennsylvania voters after switching in 2009 from Republican to Democrat. He explained the move by saying the Republican Party had become too conservative

Biden, a former U.S. senator from Delaware, recalled knowing Specter for decades in the Senate.

"I was Arlen's friend," he said. Turning to Specter's family in the front row of the sanctuary, he said: "Your father was a great man."

Sinatra's iconic tune was played as the flag-draped mahogany casket was wheeled to a hearse.

"He is survived by our memory of his will," his son Shanin, a lawyer like his father, told the congregation at Har Zion Temple in the leafy suburb of Lower Merion.

"'Never give in' was Arlen Specter's mantra," he said. "He was the patron saint of lost causes."

The service was followed by an 87-car procession to a Philadelphia-area cemetery.

"He was the fairest boss I ever had," said Erin Buechel Wieczorek, 34, of Washington, a former Senate aide who arrived at the funeral with her 7-week-old son. "I loved working for him."

(Editing by Ellen Wulfhorst and Xavier Briand)