Teaching JKPSC Lecturership Mock Test Series 2024-25 Mathematical Science Complex Analysis Contour Integral & Theorem
If f(z) is an analytic function within and on a simple closed contour C and a is any point inside C, then the integral \(\int_C \frac{f(z)}{(z-a)^2} d z \) is equivalent to:
1
\(\int_C \frac{f^{\prime}(z)}{(z-a)^2} d z\)
2
\(\int_C \frac{f^{\prime}(z)}{(z-a)} d z\)
3
\(\frac{1}{2 \pi i} \int_C \frac{f^{\prime}(z)}{(z-a)^2} d z\)
4
\(3 \pi i \int_C \frac{-f^{\prime}(z)}{(z-a)^2} d z\)