Teaching DSSSB TGT Mock Test 2025 Mathematical Science Complex Analysis Taylor Series, Laurent Series
Consider the function f defined by f(z) = \(\rm\frac{1}{1−z−z^2}\) for z ∈ ℂ such that 1 − z − z2 ≠ 0. Which of the following statements is true?
1
f is an entire function.
2
f has a simple pole at z = 0.
3
f has a Taylor series expansion f(z) = \(\rm\displaystyle\sum_{n=0}^{\infty}\) anzn, where coefficients an are recursively defined as follows: a0 = 1, a1 = 0 and an+2 = an + an+1 for n ≥ 0.
4
f has a Taylor series expansion f(z) = \(\rm\displaystyle\sum_{n=0}^{\infty}\) anzn, where coefficients an are recursively defined as follows: a0 = 1, a1 = 1 and an+2 = an + an+1 for n ≥ 0.