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Jordan's lemma : ウィキペディア英語版 | Jordan's lemma In complex analysis, Jordan's lemma is a result frequently used in conjunction with the residue theorem to evaluate contour integrals and improper integrals. It is named after the French mathematician Camille Jordan. == Statement ==
Consider a complex-valued, continuous function , defined on a semicircular contour : of positive radius lying in the upper half-plane, centred at the origin. If the function is of the form : with a positive parameter , then Jordan's lemma states the following upper bound for the contour integral: : where equal sign is when vanishes everywhere. An analogous statement for a semicircular contour in the lower half-plane holds when .
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「Jordan's lemma」の詳細全文を読む
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