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Series solutions near an irregular singularity

  1. Mar 24, 2013 #1

    ShayanJ

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    Consider a linear differential equation of the form [itex] y''+p(x)y'+q(x)y=0 [/itex] with an irregular singularity at [itex]x_0[/itex].
    How can I found a series solution to it near [itex] x_0 [/itex]?

    Thanks
     
  2. jcsd
  3. Mar 24, 2013 #2

    HallsofIvy

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    Basic answer- you don't, there isn't one. If your differential equation has an "irregular singularity" at x0, then there is no series solution in a neighborhood of x0.
     
  4. Mar 24, 2013 #3

    ShayanJ

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    Can you explain why?

    Thanks
     
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