CVR16

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Find the residues of f(z)\, at all its isolated singular points and at infinity (if infinity is not a limit point of singular points), where f(z)\, is given by \frac{e^{i z}}{\sqrt{z}}\,

This problem is currently in dispute. A reputable source thinks the given function is not representable by a Laurent series and so the residue is not defined. Investigation is proceeding.

Note that

\frac{e^{i z}}{\sqrt{z}} = \frac{\sqrt{z}e^{i z}}{z}\,

Thus

Residue at z = 0\, = \lim_{z\to 0} (z - 0)f(z)\,
= \lim_{z\to 0} \sqrt{z}e^{i z}
= \sqrt{0}e^{i 0}
= 0\,


Main Page : Complex Variables : Residues

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