Cauchy's integral formula

1. Cauchy’s integral formula
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2. Taylor series for 푓(푧)about 푧0
푓푧= 푛=0∞ 푎푛푧−푧0 푛

3. Taylor series for 푓(푧)about 푧0 푓푧 푧−푧0= 푛=−1∞ 푎푛+1푧−푧0 푛

4. Taylor series for 푓(푧)about 푧0
퐶 푓푧 푧−푧0 푑푧= 퐶 푛=−1∞ 푎푛+1푧−푧0 푛푑푧
Where퐶:푧−푧0<푅

5. Taylor series for 푓(푧)about 푧0
퐶 푓푧 푧−푧0 푑푧= 퐶 푎0 푧−푧0 푑푧

6. Cauchy’s integral formula
퐶 푓푧 푧−푧0 푑푧=2휋푖푓푧0
∵푎0=푓(푧0)

7. Cauchy’s integral formula
퐶 푓푧 푧−푧0 푑푧=2휋푖⋅푅푒푠 푓푧 푧−푧0,푧=푧0

8. Cauchy’s integral formula
푅푒푠 푓푧 푧−푧0,푧=푧0=푓(푧0)