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My mathematics professor said that it is possible to construct a Laurent series of sqrt(z) about zero by integrating over a keyhole contour and then taking the limit R --> 0 where R radius of the inner circle. But I think he is mistaken. I dont understand how it is possible to have a Laurent series about zero, as it is a branch point.

Can someone please clarify this point, and tell me what the series is if such a series exists.

Also, then is it possible to have a laurent series for any function about its branch point by considering a similar contour.

Thanks.

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# Laurent series of Sqrt(z)

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