Apery.mws Sketch of Apéry's Proof Proof of Apéry's Recurrence Recurrence for the Left-Hand Side Recurrence for the Inner Sum System for the Right-Hand Product Recurrence for the Right-Hand Side Final Proof of the Identity and of the Second Order Recurrence Computation of Zeta(3) Using Standard Maple and the Holonomic Approach Standard Maple Holonomic Approach Comparison