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In mathematics, the Lebedev–Milin inequality is any of several inequalities for the coefficients of the exponential of a power series, found by and . It was used in the proof of the Bieberbach conjecture, as it shows that the Milin conjecture implies the Robertson conjecture. They state that if : for complex numbers β''k'' and α''k'', and ''n'' is a positive integer, then : \exp\left(\sum_^\infty k|\alpha_k|^2\right), : (n+1)\exp\left(\frac\sum_^\sum_^m(k|\alpha_k|^2 -1/k)\right), : \exp\left(\sum_^n(k|\alpha_k|^2 -1/k)\right). See also exponential formula (on exponentiation of power series). ==References== * * *. * * * (Translation of the 1971 Russian edition, edited by P. L. Duren). 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Lebedev–Milin inequality」の詳細全文を読む スポンサード リンク
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