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On Extremal Properties of the Derivatives of Polynomials and Rational Functions
Published online by Cambridge University Press: 20 November 2018
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Let p(z) be a polynomial of degree n, i. e. a finite sum of the form 
where cν are any given numbers and z=x+iy is a complex variable. To answer a question raised by the chemist Mendelieff, A. Markoff [3] proved the following theorem.
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- Research Article
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- Copyright © Canadian Mathematical Society 1964
References
1.
Bernstein, S., Sur I' ordre de la meilleure approximation des fonctions continues par des polynomes de degré donné, Mémoires de l' Académie Royale de Belgique, (2), 4(1912), 1–103.Google Scholar
2.
Erdős, P., On extremal properties of the derivative of the polynomials, Annals of Math.
41(1940), 310–313.Google Scholar
3.
Markoff, A., On a certain problem of D.I. Mendelieff, Utcheniya Zapiski Imperatorskoi Akademie Nauk. (Russia) 62 (1889), 1–24.Google Scholar
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