تباين الأخوين ماركوف

لنفرض أن ${\displaystyle P}$ هو متعدد حدود من الدرجة ${\displaystyle \leq n}$. إذًا:

${\displaystyle \max _{-1\leq x\leq 1}|P^{(k)}(x)|\leq {\frac {n^{2}(n^{2}-1^{2})(n^{2}-2^{2})\cdots (n^{2}-(k-1)^{2})}{1\cdot 3\cdot 5\cdots (2k-1)}}\max _{-1\leq x\leq 1}|P(x)|.}$

• N.I.Achiezer (Akhiezer), Theory of approximation, Translated from the Russian and with a preface by Charles J.~Hyman, Dover Publications, Inc., New York, 1992. x+307 pp.
• A.A.Markov, On a question by D.I.Mendeleev, Zap. Imp. Akad. Nauk SPb. 62 (1890), 1-24
• V.A.Markov, O funktsiyakh, naimeneye uklonyayushchikhsya ot nulya v dannom promezhutke (1892). Appeared in German with a foreword by سيرغي ناتانوفيتش بيرنشتين as Über Polynome, die in einem gegebenen Intervalle möglichst wenig von Null abweichen, Math. Ann. 77 (1916), 213-258

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