Complex integration lemma: shorter proof?
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The black line is the branch cut. Lemma $$lim_{Deltato0^+}left(int_{gamma_1}+int_{gamma_2}right)f(z)ln(z-s)dz=-2pi iint_{pe^{itheta}}^{qe^{itheta}}f(t)dt$$ where $arg(z-s)in[theta,theta+2pi)$ , $f$ being holomorphic on the path of integration. Many advanced users on this site use this lemma without stating, letting alone proving it. I wrote a proof here, but it is quite long. Is there a shorter proof of this lemma?
complex-analysis complex-integration
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asked Nov 19 '18 at 0:27
Szeto
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