Complex Analysis: Dogbone Contour Generalisation

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Today, we come up with a very nice generalisation for an integral using the dogbone contour from complex analysis.

Dogbone contour example:
Residue at Infinity:
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Комментарии
Автор

I am trying to calculate the integral (x^2-1)^(-1/2) from -1 to 1 and have difficulties to find out the arg(z+1) and arg(z-1) on the interval (-1, 1) by doing what you are saying in this and the last video. Can you please tell me what the arguments of z+1 and z-1 are from above and below on the interval (-1, 1)?

By the way a very nice and clear presentation of this integral!

FunctionalIntegral
Автор

Great generalization! Can you resolve this integral (sen x)^n for odd and even numbers in your next video?😀

ldego_