hi everyone, i have a question here regarding to my topic.
I know that we could solve improper integral from -infinity to infinity by drawing a contour around the real axis and a big semi circle with R-->infinity to join the end of real infinity and real -infinity. however if there is a pole on the real axis, we need to make a small semi circle to 'skip' the pole.
The integration of this small semi circle on a single pole is given by (pi)(i)(Res(f,a)) where a is the position of the pole in the real axis.
May i know how should i approach the similar question but with repeated pole on point a now? can i still using the formula (pi)(i)(Res(f,a)) ?
I have checked the prove for this formula, it is initially assume that there is only a single pole at point a. That's why I not sure whether I could apply the same formula for a repeated pole?
Thank you everyone =)