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Homework Help: Are these analytic? (easy stuff)

  1. Sep 28, 2009 #1
    1. The problem statement, all variables and given/known data

    I have p(x)=1/x and q(x)=1/4x

    I want to know if these are analytic.
    My definition of analytic is this:
    Analytic means can be expanded in a taylor series about x=x0, with non zero radius of convergence)

    reason for asking is I want to determine whether I should use basic power series or method of frobenius for the DE:
    y'' + (1/x)y'+(1/4x)y = 0

    3. The attempt at a solution
    I'm guessing that since p and q cannot be expanded in a taylor series, that makes them non-analytic?
  2. jcsd
  3. Sep 29, 2009 #2


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    not at x = 0, i don't think so
  4. Sep 29, 2009 #3
    which is what I thought, which makes them singular points.

    Interestingly, if I use the Frobenius method, my solution ends up being the general power series :S
  5. Sep 29, 2009 #4


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    they are regular singular points though
  6. Sep 29, 2009 #5
    yes sorry.
    regular singular points which corresponds to the use of method of frobenius
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