The personal-computer business is all dressed up for Christmas, and December looks like a good month for sales. But it might have more to do with Uncle Sam than with Father Christmas.

Retailers and analysts expect sales of personal computers in the fourth-quarter will climb at least 20 percent above the year-ago mark. The major impetus for the gain, however, will come from business owners rushing to buy equipment in order to qualify for 1985 tax credits.

"They'll probably sell plenty of computers, but they won't be under the Christmas tree," said Efrem Sigel, publisher of Communications Trends in Larchmont, N.Y., which tracks computer advertising outlays.

Christmas always has been the best time of year in the personal-computer business, and the fourth quarter has long accounted for a disproportionate share of the year's sales. This year won't be much different.

But the continued flatness in sales of computers for personal use has made Christmas itself less of a factor in the industry's sales picture, said William Ablondi, vice president at Future Computing, a market research firm in Dallas. He attributes this to consumers' well-documented doubts about the computer's usefulness at home.

Ablondi projects that home-computer sales will actually decline slightly, to $1.7 billion from $1.8 billion, in the current quarter from the same period last year. But office sales, he said, will leap by one-third to $4.4 billion from $3.4 billion -- most of it in December.

If sales are slower on the home front, it won't be for the industry's lack of effort. Like last year, industry leaders IBM, Apple and Commodore are undertaking major advertising campaigns and already are cutting prices.

Software companies that have survived the industry shakeout are thriving on the holidays.

At the 234-store Toys R Us chain, sales of computer-related products are modestly higher than last year, a fact that Southern California regional manager Kip Power attributed to price cuts. One pleasant surprise is Coleco Industries' discontinued Adam computer, which is selling better than last year, Power reported. Strong sales of Commodore's new C-128 computer is the other major bright spot.

Power and other retailers said that whatever strength is shown in home sales will result from discounting, including on such discontinued products as the Adam and IBM's PCjr. A complete PCjr system can be had for around $650, while a fully equipped Adam is running $299. Apple has slashed prices by 10 percent to 35 percent on the Apple II line and its Macintosh.

"Discounting has made a lot of these products sell. That has accounted for our increase," Power said.