Proof that poles on real axis count as "half" a residue when evaluating real integrals
50057
Complex analysis and Cauchy Residue theorem
52217
Residue of two functions
127711
Evaluating $\int_{0}^{1}\int_{0}^{1}\sqrt{x^{2}+y^{2}}dxdy$ using polar coordinates.
112868
calculate an integration by using residue theorem
108872
Residues of $z^2\sin(\frac{1}{z})$
110602
A nasty integral of a rational function
153283
Trigonometric Integral Using Residue Theorem
126236
General closed form of $\int_{0}^{\theta_0} \frac{1}{\sqrt{\cos \theta-\cos \theta_0}} d\theta$
114245
What might I use to show that an entire function with positive real parts is constant?
34095
Calculating residue of pole of order $2$
39583
ii) Show that $u$ is not a real part of the function which analytic on $\mathbb{C} \backslash \lbrace 0 \rbrace$
18611
An analytic function with a simple pole
158502
Showing $\sin(\bar{z})$ is not analytic at any point of $\mathbb{C}$
140638
Integrating $\int_0^{\infty} \frac{dx}{1+x^3}$ using residues.
71540
Real and Imaginary Parts of tan(z)
66087
Calculus of residue of function around poles of fractional order (complex analysis)
68617
Show that an entire function that is real only on the real axis has at most one zero, without the argument principle