Laurent series

👨🏻‍🏫 學術台數學

嘲喃

2010-01-16 4:34 pm

Find the coefficients A_(-1),A_0,and A_1, of the Laurent series
sigma{An*z^n} n=-infinity~+infinity
of secz in pi/2<lzl<3pi/2

回答 (4)

天助

2010-01-17 11:12 am

✔ 最佳答案

Find the coefficients A_(-1),A_0,and A_1, of the Laurent series
sigma{An*z^n} n=-infinity~+infinity
of secz in pi/2<lzl<3pi/2
secz=1/cosz
=1/[1-z^2/2 + z^4/24+...]
(用長除法得)
= 1+ z^2/2 + (4/24)z^4+...

故 A(0)=1, A(1)=A(-1)=0=A(3)=A(5)..., A(2)= 1/2, A(4)=5/24, ...

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