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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lebedev-Milin inequalities ： ウィキペディア英語版 Lebedev–Milin inequality 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 :$\backslash sum\_\; \backslash beta\_kz^k\; =\; \backslash exp\backslash left(\backslash sum\_\; \backslash alpha\_kz^k\backslash right)$ for complex numbers β''k'' and α''k'', and ''n'' is a positive integer, then :$\backslash sum\_^|\backslash beta\_k|^2\; \backslash le$ \exp\left(\sum_^\infty k|\alpha_k|^2\right), :$\backslash sum\_^|\backslash beta\_k|^2\; \backslash le$ (n+1)\exp\left(\frac\sum_^\sum_^m(k|\alpha_k|^2 -1/k)\right), :$|\backslash beta\_n|^2\; \backslash le$ \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 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.