For the Laurent series for about .

The convergence region is the disc with center in z=-2 and , since we have singularities in z=3 and z=-2.

Is this correct?

The textbook unswer is that the series converges for

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- Apr 28th 2011, 02:18 PMhurzf(z)=(z-3)sein(1/(2+z))
For the Laurent series for about .

The convergence region is the disc with center in z=-2 and , since we have singularities in z=3 and z=-2.

Is this correct?

The textbook unswer is that the series converges for - Apr 28th 2011, 03:35 PMTheEmptySet
The function only has only one singularity and it is at . is an entire function with a zero at 3.

- Apr 29th 2011, 12:16 AMchisigma
Setting...

http://quicklatex.com/cache3/ql_86a4...0fa22b0_l3.png (1)

... You obtain...

http://quicklatex.com/cache3/ql_1a32...b2078b6_l3.png (2)

... so that is...

http://quicklatex.com/cache3/ql_493b...45b24b1_l3.png (3)

The (3) converges everywhere is http://quicklatex.com/cache3/ql_0571...c037d33_l3.png and has at z=-2 an essential singularity...

Kind regards