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Mathematics
Calculus
Can Laurent-Puiseux series be computed for annular regions?
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[QUOTE="jackmell, post: 3613486, member: 246161"] For example, consider: [tex]f(z)=\sqrt{z(z-1)(z-2)}[/tex] It's easy to compute the Laurent-Puiseux series in the unit disc, up to the singular point at z=1: [tex]f(z)=\sqrt{2} \sqrt{z}-\frac{3 z^{3/2}}{2 \sqrt{2}}-\frac{z^{5/2}}{16 \sqrt{2}}-\frac{3 z^{7/2}}{64 \sqrt{2}}-\frac{37 z^{9/2}}{1024 \sqrt{2}}+\cdots,\quad |z|<1[/tex] That's done by creating a differential equation for the function with polynomial coefficients then solving it using power series where in this case, the indical equation has a root c=1/2 to generate the fractional powers. But can we generate a Laurent-Puiseux series for the function in the annular region [itex]1<|z|<2[/itex]? I haven't found any info on the net about this and was hoping someone here could shed some light on the matter. Thanks, Jack [/QUOTE]
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Can Laurent-Puiseux series be computed for annular regions?
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