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Simple indicial eq

  1. Nov 17, 2008 #1
    :redface:what is the indicial equation associated with regular singularities x=1 and x=-1 of legendre's eq.?
    (1-x^2)y''-2xy'+a(a+1)y=0
     
  2. jcsd
  3. Nov 17, 2008 #2

    HallsofIvy

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    What have you done to try to find it yourself?

    If you write
    [tex]y= \sum_{n=0}^\infty a_n x^{n+c}[/itex]
    what are y' and y"? What do you get when you put those into the equation?
    Assuming a_0 is not 0, what is the coefficient of the lowest power of x in that equation?
     
  4. Nov 17, 2008 #3
    Don't they have a general formula for indicial equation for the Legendre's equation. I remember they have such a formula for Euler-Cauchy differential equation.
     
  5. Nov 18, 2008 #4
    HallsofIvy, thats the series solution for singularity x=0, if we are esprcially working for singularity x=1 or -1 than indicial would be different or not?
     
  6. Nov 18, 2008 #5

    HallsofIvy

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    Yes, I was using the most common application as an example. If a differential equation has a singularity at x= x0 you would use
    [tex]y= \sum_{n=0}^\infty a_n (x- x_0)^{n+ c}[/tex]
     
    Last edited: Nov 23, 2008
  7. Nov 23, 2008 #6
    thx a lot for ur help!
     
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