![SOLVED: Let Cr be the semi-circle of radius and centre Z0, i.e. Show that if f(z) has simple pole at Zo; then = Zo +reie ,0 < 0 < T. lim r-0 SOLVED: Let Cr be the semi-circle of radius and centre Z0, i.e. Show that if f(z) has simple pole at Zo; then = Zo +reie ,0 < 0 < T. lim r-0](https://cdn.numerade.com/ask_images/d5a7be8af03940a9aa7bf911146b2ee3.jpg)
SOLVED: Let Cr be the semi-circle of radius and centre Z0, i.e. Show that if f(z) has simple pole at Zo; then = Zo +reie ,0 < 0 < T. lim r-0
Why does the term [math]2 \pi i[/math] pop up in many cases while using the residue theorem and the Cauchy integral formula? - Quora
![integration - Improper integrals with singularities on the REAL AXIS ( Complex Variable) - Mathematics Stack Exchange integration - Improper integrals with singularities on the REAL AXIS ( Complex Variable) - Mathematics Stack Exchange](https://i.stack.imgur.com/0Q3va.png)
integration - Improper integrals with singularities on the REAL AXIS ( Complex Variable) - Mathematics Stack Exchange
![Real integral evaluation via the residue theorem with two branch points and a log-squared term – Residue Theorem and friends Real integral evaluation via the residue theorem with two branch points and a log-squared term – Residue Theorem and friends](http://residuetheorem.com/wp-content/uploads/2015/10/doublecut.jpg)
Real integral evaluation via the residue theorem with two branch points and a log-squared term – Residue Theorem and friends
![SOLVED: Recall the rule for evaluating coniour integral when the contour passes through simple pole: the net result is ZxiX residues. For example consider the following f dr = Zd= around the SOLVED: Recall the rule for evaluating coniour integral when the contour passes through simple pole: the net result is ZxiX residues. For example consider the following f dr = Zd= around the](https://cdn.numerade.com/ask_images/17bf36a425f540bdb970ddc6b468332f.jpg)