Louisiana's first presidential primary, which has produced yawns instead of soul-stirring debate, will be held Saturday, and President Carter and Ronald Reagan are expected to win easily.

The legislature set up the contest to draw candidates, media and assorted hangers-on to Louisiana and to bring in money and publicity during the slack post-Mardi Gras season of Lent. But except for two-day swings through the state this week by Reagan and George Bush, the other candidates have stayed away, preferring to campaign in the White House Rose Garden or in states with bigger delegate prizes.

The Republican candidates are vying for 31 delegates, and the Democrats for 51.

Apathy toward this primary reached such an extent that Secretary of State James H. Brown Jr. issued a press release saying how boring the event has become, and several political veterans -- including state Democratic party chairman Jesse Bankston -- have speculated that Louisiana's first primary may be its last. That will be up to the legislature, which will convene later this month.

Louisiana Republicans, who gave 36 of the 41 delegate votes they had in 1976 to the former California governor at the convention that year, may give all of this year's delegate votes to him. Except for a comparatively small number of conservative-to-moderate Republicans in New Orleans' Garden District, most party members in this state respond warmly to Reagan's conservative gospel: cut regulations, cut taxes, cut red tape and eliminate restrictions on the oil industry.

Gov. David C. Treen, who last month became Louisiana's first GOP governor in 103 years, is urging the state's Republicans to stay uncommitted until they get to the national convention in Detroit, but he told Reagan Tuesday that he will work for him if Reagan gets the nomination.

Of the state's nearly 2 million voters, about 110,000 are registered Republicans. Because of Treen's success last year against formidable Democratic candidates and because of the popularity of Reagan's conservatism, Reagan is given a good chance to win Louisiana's 10 electoral votes in November, if he is the GOP nominee.

On the Democratic side, Carter, because he is a southerner, can count on winning virtually all of this state's Democratic convention delegates. He won 35 out of 41 in 1976.

No Democratic candidate has campaigned in Louisiana, but Sen. Edward M. Kennedy sent his children and other young relatives to stump the state and tour areas damaged by recent flooding. However, that probably will not be able to overcome the Massachusetts Democrat's personal problems here -- especially lingering skepticism about his attempts to explain Chappaquiddick -- and his lack of any strong campaign organization in the state.

Besides Kennedy and Carter, the Democratic candidates on the ballot are California Gov. Edmund (Jerry) Brown Jr., who dropped out of the race Tuesday night, former Mississippi governor Cliff Finch, Richard B. Kay of Ohio, Robert E. (Bob) Maddox Jr. of Florida and Don Reaux of Texas.

In the Republican field, the only man besides Reagan and Bush with any name recognition is Harold Stassen, the perennial candidate who is making his seventh presidential campaign. The others are C. Leon Pickett of Texas, Benjamin Fernandez of California and Nick Belluso of Georgia, who has billed himself as the "self-proclaimed kook candidate."

On Saturday, the Republicans will select their convention delegates on a winner-take-all basis in each of Louisiana's eight congressional districts. In addition to the three delegates per district to be selected this way, the remaining seven will be allocated proportionally among the candidates who receive more than 25 percent of the overall vote.

Democrats will vote on candidates with delegates to be picked in April 19 caucuses in each congressional district in proportion to the number of votes their candidates received. The party's state central committee will pick the other 16 to round out representation of women and minorities.