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किसी धनात्मक पूर्णांक p के लिए निम्न सममितीय (होलोमॉर्फिक) फलन पर विचार करें

\(f(z)=\frac{\sin z}{z^p}\) \(z \in \mathbb{C} \backslash\{0\}\) के लिए

p के किन मानों के लिए ऐसा सममितीय (होलोमॉर्फिक) फलन g ∶ \(\mathbb{C}\) \{0} → \(\mathbb{C}\) है कि f(z) = g'(z) सभी z ∈ \(\mathbb{C}\) \{0} के लिए?

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CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  1. सभी सम पूर्णांक
  2. सभी विषम पूर्णांक
  3. 3 के सभी गुणज
  4. 4 के सभी गुणज

Answer (Detailed Solution Below)

Option 2 : सभी विषम पूर्णांक
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Q1.Let f be an entire function. Which of the following statement is FALSE?
Q2.किसी धनात्मक पूर्णांक p के लिए निम्न सममितीय (होलोमॉर्फिक) फलन पर विचार करें \(f(z)=\frac{\sin z}{z^p}\) \(z \in \mathbb{C} \backslash\{0\}\) के लिए p के किन मानों के लिए ऐसा सममितीय (होलोमॉर्फिक) फलन g ∶ \(\mathbb{C}\) \{0} → \(\mathbb{C}\) है कि f(z) = g'(z) सभी z ∈ \(\mathbb{C}\) \{0} के लिए?

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