CVCI6

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\oint_{|z|=1} e^{1/z}\sin\frac{1}{z} dz\,

In taylor series,

e^{1/z} = 1+\frac{1}{z} + \frac{1}{2!z} + ...\,

\sin\frac{1}{z} = \frac{1}{z} - \frac{1}{3!z^3} + ...\,

There is an essential singularity at z=0\,

The residue at z = 0 is the coefficient of 1 / z in the Laurent series of the integrand, which is 1.

So \oint = 2\pi i.

Main Page : Complex Variables : Complex Integrals

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