10:40 AM PT -- 4/13 -- Sources with direct knowledge tell TMZ ... Jamie Foxx "is doing a lot better," even joking with his family. That said, we're told the medical emergency was serious, and doctors still haven't gotten to the bottom of what happened to him. We're told he'll be in the hospital for at least a few more days, while doctors perform tests.

6:29 PM PT -- Sources with direct knowledge tell TMZ ... Jamie Foxx suffered a "medical emergency" Tuesday morning and was taken to the hospital. We're told his condition was serious enough that Jamie's family -- some of whom were not in town -- came to the hospital. One source told us, "He's communicating now, and that's good news."

Jamie Foxx suffered what his family is calling a "medical complication" ... though his daughter says her famous father's condition is already improving.

Jamie's daughter, actress Corinne Foxx, posted the medical update Wednesday on social media ... and she says Jamie suffered the issue Tuesday but immediately got "great care" and is now on the mend.

Sources with direct knowledge tell TMZ ... the condition was serious enough that Jamie was hospitalized.

Corinne adds ... "We know how beloved he is and appreciate your prayers. The family asks for privacy during this time."

At this time, it's unclear exactly how Jamie came to discover the still unspecified complication, or if he was experiencing symptoms that prompted him to get checked out.

We do, however, know Jamie's been working in Atlanta on a film called "Back in Action" with costars Glenn Close and Cameron Diaz.

It's unclear how long Jamie will need to remain in the hospital, or if and when he'll be able to return to working on the movie.

Jamie Foxx remains hospitalized more than 3 weeks after suffering a medical emergency, and those closest to him say he needs all the prayers and well-wishes his fans can muster.

While his exact condition remains secret -- tightly guarded by his family -- we've spoken with sources close to Jamie who echo the same plea -- "Pray for Jamie."

It was April 12 when Foxx's daughter, Corinne, announced her father suffered a "medical complication."

Jamie is one of the most prolific players in Hollywood, and his condition has sent studios scrambling.

Jamie has been the host of the hugely popular "Beat Shazam" music lyric game show on FOX, which was going into production just days after he was hospitalized.

Sources with direct knowledge tell us ... Jamie will not be on this season of "Beat Shazam." We're told filming starts today, with a new host. We're also told Corinne, who DJs on the show, will not be on as well -- she's been a fixture at the hospital in Atlanta by her dad's side.

As we reported, Jamie was in Atlanta for work on the film "Back in Action" when he fell ill, a stunt double and body double have been seen filling in for Jamie for that project.

Pray for Jamie.