Geodesic
Very Hyperbolic Polynomials
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 3, pp. 80-84.

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A real polynomial in one variable is hyperbolic if it has only real roots. A function $f$ is a primitive of order $k$ of a function $g$ if $f^{(k)}=g$. A hyperbolic polynomial is very hyperbolic if it has hyperbolic primitives of all orders. In the paper, we prove a property of the domain of very hyperbolic polynomials and describe this domain in the case of degree $4$.
Keywords: hyperbolic polynomial, very hyperbolic polynomial. 
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V. P. Kostov. Very Hyperbolic Polynomials. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 3, pp. 80-84. http://geodesic.mathdoc.fr/item/FAA_2005_39_3_a7/

[1] Kostov V. P., Serdica Math. J., 25 (1999), 47–70 | MR | Zbl