q-Apery Irrationality Proofs by q-WZ Pairs
  Using WZ forms, Apery-style proofs of the irrationality of the q-analogues of the Harmonic seires and Ln(2) are given. For the q-analogue of Ln(2), this method of proof produces an improved irrationality measure. 
Tewodros Amdeberhan (Temple University), Doron Zeilberger