Teaching DSSSB TGT Mock Test 2025 Mathematical Science Complex Analysis Taylor Series, Laurent Series
Let \(\rm f(z) = (1-z) e^{\left(z+\frac{z^2}{2}\right)}\)= \(\rm 1+\sum_{n=1}^{\infty} a_n z^n\).
Which of the following is FALSE?
1
\(f^{\prime}(z)=-z^2 e^{\left(z+\frac{z^2}{2}\right)}\)
2
a1 = a2
3
an ∈(-∞, 0]
4
\(\sum_{n=3}^{\infty}\left|a_n\right|<1\)