- #1
squaremeplz
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Homework Statement
describe the laurent series for the function
[tex] f(z) = z^3 cos(\frac {1}{z^2}) [/tex]
b) use your answer to part a to compute the contour integral
[tex] \int z^3 cos(\frac {1}{z^2}) dz [/tex]
where C is the unit counter-clockwise circle around the origin.
Homework Equations
The Attempt at a Solution
a)
[tex] f(z) = z^3 * \sum_{n=0}^\infty \frac {(-1)^n}{(2n)!} * ( \frac {1}{z^2} )^2^n [/tex]
[tex] f(z) = \sum_{n=0}^\infty \frac {(-1)^n}{(2n)!} * \frac {1}{z^n} [/tex]
b) so would I just evaluate
[tex] \sum_{n=0}^1 \frac {(-1)^n}{(2n)!} * \frac {1}{z^n} [/tex]
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