Let be a polynomial with non negative real coefficients, in two indeterminates. One shows that the knowledge of the poles of the integrals
gives some of the roots of the Bernstein polynomial of . One can calculate poles of these integrals using some Mellin’s methods. Some explicit computations are given.
On considère un polynôme , à coefficients réels non négatifs, à deux indéterminées. On montre que la connaissance des pôles des intégrales
donne des renseignements sur les racines du polynômes de Bernstein de . La détermination des pôles des intégrales peut se faire en utilisant certaines méthodes de Mellin. Des calculs explicites sont donnés.
@article{AIF_1986__36_4_1_0, author = {Cassou-Nogu\`es, Pierrette}, title = {Racines de polyn\^omes de {Bernstein}}, journal = {Annales de l'Institut Fourier}, pages = {1--30}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {36}, number = {4}, year = {1986}, doi = {10.5802/aif.1067}, mrnumber = {88c:32012}, zbl = {0597.32004}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.1067/} }
TY - JOUR AU - Cassou-Noguès, Pierrette TI - Racines de polynômes de Bernstein JO - Annales de l'Institut Fourier PY - 1986 SP - 1 EP - 30 VL - 36 IS - 4 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1067/ DO - 10.5802/aif.1067 LA - fr ID - AIF_1986__36_4_1_0 ER -
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. http://www.numdam.org/articles/10.5802/aif.1067/
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