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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
:C_R = \
of positive radius lying in the upper half-plane, centred at the origin. If the function is of the form
:f(z) = e^ g(z) , \quad z \in C_R ,
with a positive parameter , then Jordan's lemma states the following upper bound for the contour integral:
:\left| \int_ f(z) \, dz \right| \le \frac M_R \quad \text \quad M_R := \max_ \left| g \left(R e^\right) \right| .
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)
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