  The space of polyharmonic Maass forms was introduced by Lagarias-Rhoades,
recently. They constructed its basis from the Taylor coefficients of the real
analytic Eisenstein series. In this paper, we introduce polyharmonic weak Maass
forms, that is, we relax the moderate growth condition at cusp, and we
construct a basis as a generalization of Lagarias-Rhoades' works. As a
corollary, we can obtain a preimage of an arbitrary polyharmonic weak Maass
form under the xi-operator.
