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 a ₀ ≠ 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 .