On Laurent series with multiply positive coefficients

We consider the class of doubly infinite sequences {a_k}_k^∞= −∞ whose truncated sequences {a_k}_n^k= −n are 3-times positive in the sense of Pólya and Fekete for all n = 1, 2, ..., and a₀ ≠ 0. We obtain a characterization of this class in terms of independent parameters. We also find an estimate of the growth order of the corresponding Laurent series ∑_{k= −∞}^∞akz^k.