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Integrating exponetial of z over the conjugate of z
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[QUOTE="jackmell, post: 4510923, member: 246161"] Outstanding. Better than my way. But you could have stopped at just: [tex]\oint_{|z|=r} e^{z^2/r^2}dz=0, \quad r>0[/tex] since it's holomorphic. And also, not hard to numerically verify it in Mathematica in case you need to check something else that's not so obvious: [code] In[1]:= NIntegrate[Exp[z/Conjugate[z]]*I*Exp[I*t] /. z -> Exp[I*t], {t, 0, 2*Pi}] During evaluation of In[1]:= NIntegrate::ncvb:NIntegrate failed to converge to prescribed accuracy after 9 recursive bisections in t near {t} = {1.1269*10^-7}. NIntegrate obtained -4.996*10^-16-1.27676*10^-15 I and 3.849598995114243`*^-12 for the integral and error estimates. >> Out[1]= -4.996003610813204*^-16 - 1.27675647831893*^-15*I [/code] That's basically zero. [/QUOTE]
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Integrating exponetial of z over the conjugate of z
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