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मानें कि p एक धनात्मक पूर्णांक है। संवृत वक्र r(t) = eit, 0 ≤ t < 2π पर विचार करें। मानें कि f ऐसा फलन है जो {z ∶ |z| < R} में सममितीय (होलामॉर्फिक) है जहां R > 1 है। यदि f के शून्य केवल z0 में हो, z0 ≠ 0, |z0| < R, और उसकी बहुकता (multiplicity) q हो, तब

\(\frac{1}{2 π i} \int_r \frac{f^{\prime}(z)}{f(z)} z^p d z\)

का मान निम्न है

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CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  1. \(q z_0^p\)
  2. \(z_0 q^p\)
  3. \(p z_0^q\)
  4. \(z_0 p^q\)

Answer (Detailed Solution Below)

Option 1 : \(q z_0^p\)
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