2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65434A domain $G\subset \bar\mathbb C$ is the domain of holomorphy of the generating function of a Pólya frequency sequence of order $r$ if and only if it satisfies the following conditions: (A) $G$ contains the point $z=0$, (B) $G$ is symmetric with respect to the real axis, (C) $T=dist(0,\partial G)\in \partial G$.14 pages. To appear in PositivityComplex VariablesClassical Analysis and ODEs30B10,30B40text