Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Complex Analysis Theorems of Complex analysis
Let f : {z| |z| < 1} → ℂ be a non-constant analytic function. Which of the following conditions can possibly be satisfied by f ?
1
\(f\left(\frac{1}{n}\right)=f\left(\frac{-1}{n}\right)=\frac{1}{n^2}\) ∀ n ∈ ℕ
2
\(f\left(\frac{1}{n}\right)=f\left(\frac{-1}{n}\right)=\frac{1}{2 n+1} \) ∀ n ∈ ℕ
3
\(\left|f\left(\frac{1}{n}\right)\right|<2^{-n}\) ∀ n ∈ ℕ
4
\(\frac{1}{\sqrt{n}}<\left|f\left(\frac{1}{n}\right)\right|<\frac{2}{\sqrt{n}} \) ∀ n ∈ ℕ
5
Question Not Attempted