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Example:

[tex]f(z)=-iz\cdot\sqrt[4]{1-\frac{1}{z^{4}}}[/tex]

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- Thread starter bernardbb
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- #1

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Example:

[tex]f(z)=-iz\cdot\sqrt[4]{1-\frac{1}{z^{4}}}[/tex]

- #2

Hurkyl

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(p.s. about what point are you trying to find an expansion?)

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Around any point a with |a|>1.

As far as I know, the principal nth root of z is defined as [tex]\sqrt[n]{|z|}e^{\frac{1}{n}i\mathrm{Arg}z}[/tex], which doesn't seem very helpful; how would you expand [tex]\sqrt{z}[/tex] around a point where it is defined?

Perhaps these are silly questions; my book is very vague on Laurent expansions...

EDIT: I think I've got it... or maybe not...

As far as I know, the principal nth root of z is defined as [tex]\sqrt[n]{|z|}e^{\frac{1}{n}i\mathrm{Arg}z}[/tex], which doesn't seem very helpful; how would you expand [tex]\sqrt{z}[/tex] around a point where it is defined?

Perhaps these are silly questions; my book is very vague on Laurent expansions...

EDIT: I think I've got it... or maybe not...

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- #5

HallsofIvy

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It's essential Taylor's series, allowing negative powers.

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