You haven't told us how much deck the post in question is supporting. Is the deck 4 feet deep, or is it 16? A 15' span is not a small concept, and you are probably looking at a beam on the order of something close to a 6x14 or greater in size. (This is not a one or two man beam to lift up there, either!)
You are probably also looking at reinforcing your post footings on your other two posts, and replacing the (4x4?) posts with 6x6's. You also don't say how tall the posts are, (the amount of weight a post can bear is a function of it's cross section in square inches, ie: a 4x4 is 3.5 x 3.5, or roughly 12 square inches, and a function of its length.)
All of these specific mentionings of size are pure guesses, and are not reliable without the other information. You also don't mention what the wood is made of, the 800 gallon hot tub (6,400 pounds!), or the fact that the joists are really cantelevered floor joists from the house!
So, I can't answer your question, but these things are SOME of the factors...
Have a professional come out, and pay him to tell you what size material to use.