Racines de polynômes de Bernstein
Annales de l'Institut Fourier, Volume 36 (1986) no. 4, pp. 1-30.

Let P be a polynomial with non negative real coefficients, in two indeterminates. One shows that the knowledge of the poles of the integrals

0101x1β1-1x2β2-1P(x1,x2)sdx1dx2

gives some of the roots of the Bernstein polynomial of P. One can calculate poles of these integrals using some Mellin’s methods. Some explicit computations are given.

On considère un polynôme P, à coefficients réels non négatifs, à deux indéterminées. On montre que la connaissance des pôles des intégrales

0101x1β1-1x2β2-1P(x1,x2)sdx1dx2

donne des renseignements sur les racines du polynômes de Bernstein de P. La détermination des pôles des intégrales peut se faire en utilisant certaines méthodes de Mellin. Des calculs explicites sont donnés.

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Cassou-Noguès, Pierrette. Racines de polynômes de Bernstein. Annales de l'Institut Fourier, Volume 36 (1986) no. 4, pp. 1-30. doi : 10.5802/aif.1067. https://aif.centre-mersenne.org/articles/10.5802/aif.1067/

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