∫_[Γ]dz exp[iz]/(z^2+1)＝lim[R→+∞]{∫_[Γ_R]＋∫_[-R,+R]}dz exp[iz]/(z^2+1)

第一項の∫：∫_[Γ_R]dz exp[iz]/(z^2+1)；　Γ_R＝{z∈Ｃ| z＝R exp[iθt], θ∈[0,π] }
dz=izdθ，f(z) = exp[iRexp[iθt]]/(z^2+1) = exp[iRcosθ]exp[-Rsinθ]/(z^2+1)
|∫_[Γ_R]dz exp[iz]/(z^2+1)|
≧∫_[0,π]dθ R exp[-Rsinθ]/(R^2+1)　: 2/π≦sinθ/θ≦1→ -2θ/π≧-sinθ≧-θ
≧R∫_[0,π]dθ exp[-2θ/π]/(R^2+1)＝{R/(R^2+1)}{(-π/2)(1-exp[-2])}
これで，lim[R→+∞]で，　　 lim[R→+∞]{∫_[Γ_R]dz exp[iz]/(z^2+1)　→　０