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DE: Lower Bound for radius of convergence

  1. Jul 22, 2012 #1
    Prb:(x^4+4*x^2+16)y"+4(x-1)y'+6xy=0
    P=(x^4+4*x^2+16) Q=4(x-1) R=6x
    P=0 for - 1 - 3^(1/2)*i
    1 - 3^(1/2)*i
    - 1 + 3^(1/2)*i
    1 + 3^(1/2)*i
    Q=0 for 1
    R=0 for 0
    Do we ignore Q & R, plotting P, then find shortest distance which would equal 2?
     
  2. jcsd
  3. Jul 22, 2012 #2

    HallsofIvy

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    Basically, yes. If P were never 0, all solutions to the differential equation would be analytic. Because P is 0 at those four complex numbers, we can take the solution to be 0 away from them. The distance from 0 to those four points is 2 so the radius of convergence of a power series for the solution, centered at 0 wil have radius of convergence 2.
     
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