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যেকোনো বিন্দুতে f(a)-এর জন্য কশির ইন্টিগ্রাল ফর্মুলা পোলার ফর্মে হল:

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UPPCL AE Electrical 2 April 2022 Official Paper (Shift 2)
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  1. f(reiθ)dθ
  2. f(a + reiθ)dθ
  3. f(a + reiθ)dθ
  4. f(eiθ)dθ

Answer (Detailed Solution Below)

Option 3 : f(a + reiθ)dθ
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Detailed Solution

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কশির সমাকল সূত্র

যদি একটি জটিল অপেক্ষক f(z) একটি সরল-সংযুক্ত ডোমেইনের মধ্যে একটি বদ্ধ কন্টুর c-এর ভিতরে এবং তার উপর বিশ্লেষণাত্মক হয়, এবং যদি zo C-এর মাঝখানে কোনো বিন্দু হয়, তাহলে z = zo -তে f(z) এর মান দেওয়া আছে:

পোলার ফর্মে:

(z = x + iy) কে (z = reiθ) রূপে রূপান্তরিত করা হয়, যেখানে:

এবং

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