Bulletin of the Faculty of Education, Yamaguchi University. Natural science

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Bulletin of the Faculty of Education, Yamaguchi University. Natural science Volume 23 Issue 2
published_at 1973-10

On the Mean Value Theorems for the Integration of Complex-Valued Functions

複素数値関数の積分に関する平均値の定理について
Mizuno Yasuyuki
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Descriptions
[定理1]φ(z)を単連結な領域Dにおいて正則とし,Dの相異なる2点α,βを結ぶ線分rがDの点ばかりから成るとき,r上の適当な2つの内点をγ_1,γ_2とすれば ∫_<αcβ>φ(z)dz=(β-α){Reφ(γ_1)＋iI_mφ(γ_2)}が成り立つ。ここに積分路cは,αとβを結ぶD内の任意の正則曲線である。 (証明)φ(z)は単連結な領域Dで正則であるから,αを固定して考えれば,∀τ∈Dに対してαとrを結ぶD内の正則曲線cをどのようにえらんでも∫_<αcr>φ(z)はτのみの関数とな
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