< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

How would you find the radius of convergence for the taylor expansion of:

$$f(z)=\frac{e^z}{(z-1)(z+1)(z-3)(z-2)}$$

I was thinking that you would just differentiate to find the taylor expansion and then use the ratio test but this seems far too tedious to be the right way to do it! Any help?

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Svein
The Taylor expansion of ez converges for all z. The denominator introduces poles at -1, 1, 2 and 3, so you need to be sufficiently far away from those values. Now determine "sufficiently far away"...

Ray Vickson
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< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

How would you find the radius of convergence for the taylor expansion of:

$$f(z)=\frac{e^z}{(z-1)(z+1)(z-3)(z-2)}$$

I was thinking that you would just differentiate to find the taylor expansion and then use the ratio test but this seems far too tedious to be the right way to do it! Any help?

Should we assume you want to expand around ##z = 0##?

Ray Vickson
$$f(z)=\frac{e^z}{(z-1)(z+1)(z-3)(z-2)}$$