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On the real zeros of Bernoulli polynomials. (Sur les zéros réels des polynômes de Bernoulli.) (French) Zbl 0725.11011

Nous donnons les démonstrations détaillées des résultats énoncés dans une note de même titre [C. R. Acad. Sci., Paris, Sér. I 303, 539–542 (1986; Zbl 0607.10006)]. Ces résultats concernent le nombre et la position des zéros réels des polynômes de Bernoulli.

MSC:

11B68 Bernoulli and Euler numbers and polynomials
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)

Citations:

Zbl 0607.10006
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References:

[1] J. BRILLHART, On the Euler and Bernoulli polynomials, J. Reine Angew. Math., 234 (1969), 45-64. · Zbl 0167.35401
[2] H. DELANGE, Sur les zéros réels des polynômes de Bernoulli, C.R. Acad. Sc. Paris, série I, 303 (1986), 539-542. · Zbl 0607.10006
[3] K. INKERI, The real roots of Bernoulli polynomials, Ann. Univ. Turk., Ser. AI, 37 (1959), 3-19. · Zbl 0104.01502
[4] D. H. LEHMER, On the maxima and minima of Bernoulli polynomials, Amer. Math. Monthly, 47 (1940), 533-538.
[5] J. LENSE, Über die Nullstellen der Bernoullischen Polynome, Monatsh. Math., 41 (1934), 188-190.
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