I honestly don't like jungle Jax. Every time I try to gank, I get CC'd and can't get the stun off. I've also had multiple games against Jax where all I have to do is jump away after the leap strike hits and he never gets the stun off.
Anyway, I like to play Jax top with mostly AD/AP and just enough tankiness to survive in the middle of the enemy team. If they're completely ignoring you, you shouldn't need any more durability than Tri Force/Frozen Mallet. --- Generation 30: The first time you see this, copy it into your own signature (on any forum) and add one to the generation number. Social experiment.
Jax's passive gives him free attack speed, good with AD obviously.
Q scales with AD/AP.
W scales with AP.
E scales with AD.
Ult has a passive that scales with AP. The active scales with AD and AP, giving him more defense based on these two stats.
So he has the option of building nearly pure DPS and getting temporary defense with his ult. Most people opt to build AD items and AD/AP items, not usually building pure AP items. Also 1-2 defensive items work. Attack speed is also very nice to get more procs of his passive.
Trinity force Rageblade Gunblade GA
Those items are what I would call "core". They are just so good on Jax. To finish it off...
Warmogs ( league of warmogs, pure defense ) Nashor's ( pure damage between the ap, attack speed, and cdr ) Zephyr ( if you got tabis ) Black cleaver ( cdr, hp. good against high armor and/or your team is mostly physical ) Maw ( if they have a fed AP ) Blade of the Ruined King ( never used this personally, I hear good things, I guess if they have lots of warmogs ) --- #1 LoL Poster NA: http://www.gamefaqs.com/boards/954437-league-of-legends/63627116