How do you analyse for convergence/divergence on the circle of convergence of a particular power series?
circle of convergence
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complex-analysis
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0The behaviour can be quite varied; see http://en.wikipedia.org/wiki/Circle_of_convergence#Convergence_on_the_boundary. – 2011-04-05
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0But aren't there any methods that I can use to figure it out? – 2011-04-05
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2This is an interesting and delicate topic. You may want to read http://mathoverflow.net/questions/49395/behaviour-of-power-series-on-their-circle-of-convergence/ – 2011-04-05
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0Thanks a lot for that Andres :) – 2011-04-05
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0I do not know of "general" techniques. There are results that apply in particular cases (you may identify the function on the boundary with certain Fourier series, for example, or in some cases you may apply "summation by parts"). – 2011-04-05
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1Do you have specific examples in mind? – 2011-04-05