The WZ method and flawless WZ pairs

Abstract

Recently, Kam Cheong Au discovered a powerful methodology of finding new Wilf-Zeilberger (WZ) pairs. He calls it WZ seeds and gives numerous examples of applications to proving longstanding conjectural identities for reciprocal powers of $\pi$ and their duals for Dirichlet $L$-values. In this note we explain how a modification of Au's WZ pairs together with a classical analytic argument allows one to obtain simpler proofs of his results. We illustrate our method with a few examples elaborated with assistance of Maple code that we have developed.