Geodesic
Zero sets of entire generating functions of P\'olya frequency sequences of finite order
Izvestiya. Mathematics , Tome 35 (1990) no. 1, pp. 101-112.

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A full description of zero sets of entire generating functions of Pólya frequency sequences of finite order is given. A generalization to the transcendental case of Poincaré's polynomial theorem, relating to the problem of precise determination of the number of positive roots with the help of Descartes' rule, is obtained. Bibliography: 9 titles. 
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O. M. Katkova; I. V. Ostrovskii. Zero sets of entire generating functions of P\'olya frequency sequences of finite order. Izvestiya. Mathematics , Tome 35 (1990) no. 1, pp. 101-112. http://geodesic.mathdoc.fr/item/IM2_1990_35_1_a4/

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