※ 引述《DTpower (三/]\)》之銘言：
: Evaluate the integral over the given contour C,
: sin(z)
: f(z)=---------- C consists of the boundaries of the squares with
: 2 3i,-3i,3,-3 (conterclockwise and 1,-1,i,-i(clockwise).
: 4z - 8iz
: 麻煩神人了
1.令C=C1+C2
sinz
f(z)=-----------------
z(4z-8i)
令4z=8i
則z=2i：simple pole
2.
sinz sin2i 1 1
Resf(z)= lim (z-2i)f(z)=-----------=----------=------- i sinh2=------ sinh2
z->2i z->2i z 2i 2i 2
1
故所求積分∫f(z)dz=2πi(----- sinh2)=πi sinh2
2
若有錯請大大指教
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