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γ को {z ∈ \(\mathbb{C}\) ∶ |z - 1| = 1/2} से दिये जाने वाले सम्मिश्र समतल में धनात्मक रूप से अभिविन्यस्त वृत्त मान लें। तब रैखीय समाकलन

\(\int_\gamma \frac{z e^{1 / z}}{z^2-1} d z\)

निम्न के बराबर है

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CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  1. iπe
  2. -iπe
  3. πe
  4. -πe

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Option 1 : iπe
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More Contour Integral & Theorem Questions

Q1.मानें कि सम्मिश्र समतल में, C एक धनात्मक रूप से अभिविन्यस्त वृत्त है जो मूल बिंदु पर केंद्रित एवं त्रिज्या 3 का है। तब समाकलन \(\rm\displaystyle\int_C \frac{d z}{z^2\left(e^z−e^{−z}\right)}\) का क्या मान है?  
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Q3.γ को {z ∈ \(\mathbb{C}\) ∶ |z - 1| = 1/2} से दिये जाने वाले सम्मिश्र समतल में धनात्मक रूप से अभिविन्यस्त वृत्त मान लें। तब रैखीय समाकलन \(\int_\gamma \frac{z e^{1 / z}}{z^2-1} d z\) निम्न के बराबर है

More Complex Analysis Questions

Q1.The only function among the following that satisfies Cauchy's Riemann (C-R) equations is : 
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Q3.Let f be an entire function. Which of the following statement is FALSE?
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Q7.मान लीजिए f(z) = exp\(\rm\left(z+\frac{1}{z}\right)\), z ∈ ℂ\{0} है। तब f का z = 0 पर अवशेष _______ है।
Q8.मानें कि सम्मिश्र समतल में, C एक धनात्मक रूप से अभिविन्यस्त वृत्त है जो मूल बिंदु पर केंद्रित एवं त्रिज्या 3 का है। तब समाकलन \(\rm\displaystyle\int_C \frac{d z}{z^2\left(e^z−e^{−z}\right)}\) का क्या मान है?  
Q9.ऐसे z ∈ ℂ कि 1 − z − z2 ≠ 0 हो, के लिए f(z) = \(\rm\frac{1}{1−z−z^2}\) द्वारा परिभाषित फलन f पर विचार करें। निम्न वक्तव्यों में से कौन सा सत्य है?

More Mathematical Science Questions

Q1.The only function among the following that satisfies Cauchy's Riemann (C-R) equations is : 
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