What was going on when I was born?

White House officials said tonight that President Reagan was extending a ''personal invitation'' to Mikhail S. Gorbachev, the new leader of the Soviet Union, to meet in the United States in hopes of improving relations between the two countries. The officials said Mr. Reagan would ''prefer'' a meeting in the United States because talks between American and Soviet leaders over the last decade have taken place abroad. The officials said Mr. Reagan's message would be delivered Wednesday to Mr. Gorbachev by Vice President Bush, who is leading the American delegation to the funeral of Konstantin U. Chernenko, the Soviet leader, who died Sunday evening. Thoughts of Legacy A ranking White House official said Mr. Reagan ''was beginning to think about his legacy.'' The official added, ''He wants to meet Gorbachev at a mutually agreed-on date; he wants to work out an accommodation on arms control.''

An article yesterday about the use of Mahler's music in dance misidentified the theater in which the Joffrey Ballet is performing. It is the New York State Theater.

WEDNESDAY, MARCH 13, 1985 International President Reagan will seek to meet with the new Soviet leader, Mikhail S. Gorbachev, in the United States in hopes of improving American-Soviet relations. A ranking White House official said Mr. Reagan sought to meet Mr. Gorbachev ''to work out an accommodation on arms control.'' (Page A1, Columns 4-6.) World leaders gathered in Moscow to pay their respects at the bier of Konstantin U. Chernenko, who is to be buried beside the Kremlin wall today. Vice President Bush arrived bearing what he called ''a message of peace'' from President Reagan. (A1:4-5.)

Saying the Manhattan District Attorney had ''significant new evidence'' against Bernhard H. Goetz, a judge yesterday authorized a new grand jury to investigate Mr. Goetz's shooting of four teen-agers on a subway train last December. The District Attorney, Robert M. Morgenthau, refused to characterize the new evidence. But under state law a district attorney may seek a judicial order for a new grand jury only if he finds evidence that was not available to the first grand jury. The law permits a prosecutor only one additional opportunity to present a case, and a judge must review the new evidence before a new grand jury can be authorized.

The financially troubled Castle & Cooke Inc. said today that it had agreed to merge with the Flexi-Van Corporation, a transportation equipment leasing company controlled by David H. Murdock, the West Coast financier. The deal, which will create a combined company with a market value of about $600 million, is expected to help Castle & Cooke escape from severe debt problems that have threatened to drive it into bankruptcy. Under the agreement, Flexi-Van, based in New York, will become a subsidiary of Castle & Cooke, the Hawaii food and real estate company known mainly for its Dole products. Present Castle & Cooke shareholders will end up owning 55 percent of the new company, while Flexi-Van shareholders will own 45 percent on a fully diluted basis.

''We Are the World,'' the song recorded by 46 of the country's leading pop stars to aid famine- stricken African countries, is spinning right off New York shelves. The two stores of Tower Records and the four of Sam Goody all sold out within hours of the record's delivery last Thursday.

A Washington dispatch yesterday on President Reagan's medical examination, and the text of a White House statement that accompanied it, included incorrect figures issued by the White House for the President's cholesterol and alkaline phosphatase levels. The cholesterol level was 206 and the alkaline phosphatase level was 65, both ''within normal ranges,'' the White House said. The figure of 102, initially reported as Mr. Reagan's cholesterol level, was his triglyceride level, the White House said.

A report in the Briefing column of the Washington Talk page yesterday, on the Chatham House Foundation, misidentified an executive of the RCA Corporation. He is Thornton F. Bradshaw, its chairman and former chief executive officer.

Some of the strangest assets are showing up on the books of many large American corporations. Food companies are suddenly buying oil rigs and computer companies are purchasing hay balers. They are not on a buying binge for themselves, however. These corporations are among a group of new entrants in the booming business of lease financing. They are are buying the equipment for other companies that will rent the equipment back. The Olin Corporation, for instance, a maker of chemicals, brass, ammunition and skis, went into the leasing business a few months ago and will buy virtually any type of equipment for its new customers. This could include computers, drill presses, jet aircraft and everything but the walls and roof of a new steel mill.

The city's Landmarks Preservation Commission is considering creating a historic district on the Upper West Side, but is undecided on its boundaries. A proposal is before the commission to create a district that would encompass Riverside Drive and West End Avenue between 80th and 81st Streets, and both sides of 80th Street and most of the south side of 81st Street between Riverside and West End. The proposed district includes 38 buildings, many of them built in the 19th century by the developer Bernard S. Levy. The Upper West Side district, according to the landmarks commission staff, symbolizes ''a comprehensive history of the development of this area, ranging from side-street row house construction in the 1890's to the Art Moderne apartment houses that typically define the avenues on today's Upper West Side.''

Four years ago, when Elizabeth Holtzman decided to run for Brooklyn District Attorney, some people wondered how she would reconcile a liberal philosophy with the realities of what is known as a law-and-order job. This year, Miss Holtzman, who is 43 years old, expects to seek re-election as the District Attorney, a position to which she brought legislative skills learned in Congress but in which her administrative training in the overburdened criminal-justice system has been on the job. ''You can't just look at the prosecution of each individual case,'' Miss Holtzman said in an interview. ''You also have to be an advocate for the improvement of the system, to be imaginative, experimental. ''Yet you also can't be like Emerson, looking through the puddles and paying attention to the sky.''

American teen-agers become pregnant and give birth and have abortions at significantly higher rates than do adolescents in other industrialized nations, according to a study released yesterday by the Alan Guttmacher Institute. Moreover, the United States is the only developed country where teen- age pregnancy has been increasing in recent years, the study reported. The pregnancy rate for Americans 15 to 19 years old stands at 96 per 1,000, compared with 14 per 1,000 in the Netherlands, 35 in Sweden, 43 in France, 44 in Canada and 45 in England and Wales, the countries that were studied in depth as a backdrop to the experiences of American teen-agers. The teen-age abortion rate for the United States was found to be as high as the combined abortion and birth rates for the other countries studied. Although pregnancy rates among black American teen-agers are much higher than rates among white teen-agers - 163 pregnancies per 1,000 as against 83 per 1,000 - this does not account for the United States' high rates compared with industrialized nations.