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How do I understand whether a series will diverge at some point?

For example, in the Legendre's diff. equation $$(1-z^2)y' '-2zy'+\ell(\ell+1)y~=~0,$$
does $y(z)$ diverge for $z=-1$ and $z=+1$?

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  • $\begingroup$ Would Mathematics be a better home for this question? $\endgroup$
    – Qmechanic
    Commented Oct 28, 2013 at 15:16
  • $\begingroup$ Oh okay. Then I'll post it there. $\endgroup$
    – Wonder
    Commented Oct 28, 2013 at 15:18
  • $\begingroup$ Why can't I see this question in the mathematics site? $\endgroup$
    – Wonder
    Commented Oct 28, 2013 at 15:36
  • $\begingroup$ Math.SE probably rejected the migration. $\endgroup$
    – Qmechanic
    Commented Oct 28, 2013 at 15:38
  • $\begingroup$ Then how/where do I get the answer? :( $\endgroup$
    – Wonder
    Commented Oct 28, 2013 at 15:39

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