Shares of Apple, maker of the market-leading iPod digital music player and Macintosh computers, closed up $2.45 to $59.95 on the Nasdaq, a gain of more than 4 percent.

Apple dominates the digital music business it helped establish, and its growth appears to be accelerating amid concern that industry sales are less than robust.

“When everyone else is slowing and you’re not, it means share gains,” American Technology Research analyst Shaw Wu told Reuters.

In July, the company said it sold around 1.5 million songs per day. Based on recent comments from Apple Chief Executive Steve Jobs, Wu estimated that Apple was selling about 1.8 million songs per day in September.

“It’s probably closer to 2 million as we enter the holidays,” Wu said.

Compounding confidence was Apple’s announcement earlier this week that its iTunes online service sold 1 million videos in less than 20 days. The company recently released a new iPod that can play video on its 2.5-inch color screen.

“I think the 1 million video mark in 20 days gives people comfort that video isn’t a dud–that it’s being accepted,” said Rochdale Research analyst Daan Coster.

Apple’s PC business is also growing faster than the overall market.

Analysts said the upward momentum in Apple’s stock may be a result of investor movement into names already showing good results with credible prospects of growth.

“It’s the flight to quality. Investors want to own the names that are doing well,” Wu said.

Apple is “one of the few quality names out there with pretty high visibility,” said Wu, speaking of the company’s ability to forecast results with reasonable accuracy. “You know whether they’re doing well or not.”