Teaching DSSSB TGT Mock Test 2025 Mathematical Science Complex Analysis Taylor Series, Laurent Series
Which of the following is the Laurent's series of the function f(z) = \(\frac{1}{(z^2-4)(z+1)}\) in the region 1 < |z| < 2
1
f(z) = \(\frac{1}{8}\sum_{n=0}^{\infty}(-1)^n\left(\frac z2\right)^n+\frac{1}{24}\sum_{n=0}^{\infty}\left(\frac z2\right)^n\frac{1}{3z}\sum_{n=0}^{\infty}\frac{(-1)^n}{z^n}\)
2
f(z) = \(\frac{1}{8}\sum_{n=0}^{\infty}(-1)^n\left(\frac z2\right)^n-\frac{1}{24}\sum_{n=0}^{\infty}\left(\frac z2\right)^n+\frac{1}{3z}\sum_{n=0}^{\infty}\frac{(-1)^n}{z^n}\)
3
f(z) = \(-\frac{1}{8}\sum_{n=0}^{\infty}(-1)^n\left(\frac z2\right)^n-\frac{1}{24}\sum_{n=0}^{\infty}\left(\frac z2\right)^n-\frac{1}{3z}\sum_{n=0}^{\infty}\frac{(-1)^n}{z^n}\)
4
f(z) = \(\frac{1}{8}\sum_{n=0}^{\infty}(-1)^n\left(\frac z2\right)^n-\frac{1}{24}\sum_{n=0}^{\infty}\left(\frac z2\right)^n-\frac{1}{3z}\sum_{n=0}^{\infty}\frac{(-1)^n}{z^n}\)