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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 Watson's lemma ： ウィキペディア英語版 Watson's lemma In mathematics, Watson's lemma, proved by G. N. Watson (1918, p. 133), has significant application within the theory on the asymptotic behavior of integrals. == Statement of the lemma == Let be fixed. Assume $\backslash phi(t)=t^\backslash lambda\backslash ,g(t)$, where $g(t)$ has an infinite number of derivatives in the neighborhood of $t=0$, with $g(0)\backslash neq\; 0$, and $\backslash lambda\; >\; -1$. Suppose, in addition, either that : where $K,b$ are independent of $t$, or that : Then, it is true that for all positive $x$ that : and that the following asymptotic equivalence holds: :$\backslash int\_0^T\; e^\backslash phi(t)\backslash ,\; \backslash mathrm\; dt\; \backslash sim\backslash \; \backslash sum\_^\backslash infty\; \backslash frac\{n!\backslash \; x^\{\backslash lambda+n+1\}\},\backslash \; \backslash \; (x>0,\backslash \; x\backslash rightarrow\; \backslash infty).$ See, for instance, for the original proof or for a more recent development. 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「Watson's lemma」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.