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The Ap\'ery polynomials and in particular their asymptotic behavior play anessential role in the understanding of the irrationality of \zeta(3). In thispaper, we present a method to study the asymptotic behavior of the sequence ofthe Ap\'ery polynomials ((B_{n})_{n=1}^{\infty}) in the whole complex plane as(n\rightarrow \infty). The proofs are based on a multivariate version of thecomplex saddle point method. Moreover, the asymptotic zero distributions forthe polynomials ((B_{n})_{n=1}^{\infty}) and for some transformed Ap\'erypolynomials are derived by means of the theory of logarithmic potentials withexternal fields, establishing a characterization as the unique solution of aweighted equilibrium problem. The method applied is a general one, so that thetreatment can serve as a model for the study of objects related to the Ap\'erypolynomials.

Ap\'ery Polynomials and the multivariate Saddle Point Method