It actually is a coaxial digital audio jack. The connector looks just like a regular RCA plug. You might be confused by the placement. I missed it at first, too. Right next to the "digital audio out" label is a plug you can pull out with some strange-looking connector. Not sure what that is, but it's not the digital audio. The digital audio is actually to the left of the label, a black RCA-type next to a red-white RCA combo.
did the coaxial cable work when you did it? I called Sharp and the didn't have cables and said it wasn't coaxial. It does look like a regular RCA plug and if that is the case, then I'll just go by a coaxial cable.
I am working with the same TV and found out that a single regular RCA cable to the digital audio output (black color) connector to a similar single digital audio in RCA jack (Such as the one on a Bose V35) does work. The setup I'm working with has no cable box, just a coaxial cable TV cord going directly into the TV with no separate tuner system. I was able to get surround sound to work to a 5-speaker system. I would like to see how a gold coaxial RCA-type connector with a solid core (as opposed to stranded) does to deliver better audio. If I get to do that, I'll update here. Sharp might have confused coaxial cable like the kind that delivers TV signal from the cable TV company with coaxial audio cable.
I thought it was the square input, as well. Thanks for this tip, and it works great. Sharp wanted to charge me $28 to answer this question. The thing that threw me was that the manual refers to the output as coaxial. It is simply takes a single RCA cable. Wonder what that square connection is all about?